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mathematics, specifically the algebraic theory of fields, a normal basis is a special kind of basis for Galois extensions of finite degree, characterised as
Normal_basis
Topics referred to by the same term
Gröbner basis Hilbert's basis theorem Generating set of a group Base (topology) Change of basis Greedoid Normal basis Polynomial basis Radial basis function
Basis
Topics referred to by the same term
object Normal basis (of a Galois extension), used heavily in cryptography Normal bundle Normal cone, of a subscheme in algebraic geometry Normal coordinates
Normal
Basis of a type of algebraic structure
{\displaystyle AM=MJ} . Canonical form Change of basis Normal basis Normal form (disambiguation) Polynomial basis Bronson (1970, p. 196) Lusztig (1990) Kashiwara
Canonical_basis
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
respect to a basis for which the operator takes its Jordan normal form. The diagonal form for diagonalizable matrices, for instance normal matrices, is
Jordan_normal_form
Probability distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued
Normal_distribution
Type of algebraic field extension
L is a finite extension of K, then its normal closure is also a finite extension. Galois extension Normal basis Lang 2002, p. 237, Theorem 3.3, NOR 3.
Normal_extension
Mathematical terminology
equivalent to the existence of a normal integral basis, i.e. of α in OL such that its conjugate elements under G give a free basis for OL over OK. This is an
Galois_representation
Representation theory of groups
the content of the normal basis theorem, a normal basis being an element x of L such that the g(x) for g in G are a vector space basis for L over K. Such
Regular_representation
Normal standard of review in U.S. constitutional law
In U.S. constitutional law, rational basis review is the normal standard of review that courts apply when considering constitutional questions, including
Rational_basis_review
Mathematical form for PDEs
In mathematics, a Janet basis is a normal form for systems of linear homogeneous partial differential equations (PDEs) that removes the inherent arbitrariness
Janet_basis
Basis used to express spherical tensors
normal to the plane in the z direction: e 0 = e z {\displaystyle \mathbf {e} _{0}=\mathbf {e} _{z}} The inverse relations are: While giving a basis in
Spherical_basis
Probability distribution
X has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution
Log-normal_distribution
Matrix that commutes with its conjugate transpose
square matrix A is normal if it commutes with its conjugate transpose A*: A normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{ normal}}\iff A^{*}A=AA^{*}
Normal_matrix
Arbitrage strategy
as a 'basis' where the trader will profit from price discrepancies. Basis trading is also called the 'cash-and-carry trade'. In finance, the basis typically
Basis_trading
Matrix form in linear algebra
In linear algebra, the Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z {\displaystyle \mathbb {Z} } . Just
Hermite_normal_form
Mathematical construct in computer algebra
is the starting point of Gröbner basis theory. The definition of the reduction shows immediately that, if h is a normal form of f by G, one has f = h +
Gröbner_basis
A dual basis is not a specific basis like the polynomial basis or the normal basis; rather for any given basis, it is another associated basis which is
Dual basis in a field extension
Dual_basis_in_a_field_extension
Arithmetic in a field with a finite number of elements
others look quite different (for instance, using matrices). Using a normal basis may have advantages in some contexts. When the prime is 2, it is conventional
Finite_field_arithmetic
Canonical form of matrices over a field
In linear algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices
Frobenius_normal_form
Cable that provides power to electric railways, trams, and trolleybuses
different voltages or frequencies.) The grids may be synchronised on a normal basis, but events may interrupt synchronisation. This is not a problem for
Overhead_line
Special coordinate system in differential geometry
convex normal neighborhood U is a normal neighborhood of every p in U. The existence of these sorts of open neighborhoods (they form a topological basis) has
Normal_coordinates
Group comohology of Galois modules
in algebraic number theory and the arithmetic of elliptic curves. The normal basis theorem implies that the first cohomology group of the additive group
Galois_cohomology
Situation when futures prices are below the expected spot price at maturity
to "positive basis", which occurs when the current spot price exceeds the price of the future. The opposite market condition to normal backwardation
Normal_backwardation
Formulas in differential geometry
discovery. The tangent, normal, and binormal unit vectors, often called T, N, and B, or collectively the Frenet–Serret basis (or TNB basis), together form an
Frenet–Serret_formulas
Line or vector perpendicular to a curve or a surface
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve
Normal_(geometry)
GF(2m) using the normal basis representation of elements, however, it is generic and can be used for other bases, such as the polynomial basis. It can also
Itoh–Tsujii inversion algorithm
Itoh–Tsujii_inversion_algorithm
Salt water for medical purposes
widely used until decades later. The term "normal saline" itself appears to have little historical basis, except for studies done in 1882–83 by Dutch
Saline_(medicine)
Software patents of elliptic curve cryptography
expired. Certicom holds a patent on efficient GF(2n) multiplication in normal basis representation; U.S. patent 5,787,028 expired in 2016. Certicom holds
ECC_patents
German mathematician (1882–1935)
1007/BF01472227 Stauffer, Ruth (July 1936), "The Construction of a Normal Basis in a Separable Normal Extension Field", American Journal of Mathematics, 58 (3):
Emmy_Noether
Result about when a matrix can be diagonalized
can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a diagonalizable
Spectral_theorem
Species of fish
to their poor eyesight, Indian mud morays typically do not hunt on a normal basis, but will resort to hunting if there is no other option. When kept in
Indian_mud_moray_eel
In mathematics, the rational normal curve is a smooth, rational curve C of degree n in projective n-space Pn. It is a simple example of a projective variety;
Rational_normal_curve
Counts the number of necklaces of n colored beads picked from α available colors
} {\displaystyle \{x,\sigma x,...,\sigma ^{n-1}x\}} is an F-basis for L (a normal basis), where σ is the Frobenius automorphism σ y = y k {\displaystyle
Necklace_polynomial
Texture mapping technique
derivatives can be used as a basis of the tangent spaces at every point. In order to find the perturbation in the normal the tangent space must be correctly
Normal_mapping
Field theory is the branch of algebra that studies fields
Covers an exceptional case of Kummer theory, in characteristic p. Normal basis A basis in the vector space sense of L over K, on which the Galois group
Glossary_of_field_theory
Normal type (in German: Normaltyp) is a typological term in sociology coined by the German sociologist Ferdinand Tönnies (1855–1936). It can be considered
Normal_type
coordinates, for a given choice of basis (in the vector space underlying the projective space). The choice of basis means this definition is not intrinsic
Homogeneous_coordinate_ring
Risks that are uncontrollable by the first party
earthquakes and volcanoes. Insurance adjusters analyze external risks on a normal basis. Measuring risks of the environment is common practice throughout insurance
External_risk
Treasury basis trading: bond and futures arbitrage strategy
short-term repo financing. According to the FPC, while the basis trade can improve liquidity in normal conditions, it may act as a transmission channel for
Treasury_basis_trade
Species of sponge
and toxic abilities. Sponges are found to interact with bacteria on a normal basis. The bacteria found on sponges is responsible for the production of antibacterial
Suberites_domuncula
notion to create normal surface theory, which forms the basis of many algorithms in 3-manifold theory. The notion of almost normal surfaces is due to
Normal_surface
Type of photography and cinematography lens
In photography and cinematography, a normal lens is a lens that reproduces a field of view that appears "natural" to a human observer. In contrast, depth
Normal_lens
Biological processes that underlie human's perception of self-understanding
The neural basis of self is the idea of using modern concepts of neuroscience to describe and understand the biological processes that underlie humans'
Neural_basis_of_self
the neon cover being made at a normal basis, not a collectors edition. The cover is a shade of blue this time. The normal paperback version was published
The_Joshua_Files
Machine learning kernel function
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In
Radial_basis_function_kernel
Singularities of algebraic varieties
a normal crossing singularity looks locally like a union of coordinate hyperplanes. There are two variants of the concept, a divisor with normal crossings
Normal_crossing_singularity
American YouTube personality (born 1990)
webseries Game Grumps, and co-created the video game entertainment website Normal Boots. As of July 2025[update], his YouTube channel JonTronShow has 6.48
JonTron
English contract law case on damages for breach of contract
facts which should not be a sufficient ground for departing from the normal basis on which damages are awarded: the fact that the breach was cynical and
Attorney_General_v_Blake
American breed of meat goat
to prove it as fact to his neighbors. The goats were unable to jump over normal-sized fences, and found holes in the ground to crawl underneath the fences
Fainting_goat
Relative weight based on mass and height
height. Major adult BMI classifications are: underweight (under 18.5), normal weight (18.5 to 24.9), overweight (25 to 29.9), and obese (30 or more).
Body_mass_index
Type of polytope in mathematics
{\displaystyle \mathbb {R} } d+1 the following are equivalent: P is normal. The Hilbert basis of C(P) ∩ Z {\displaystyle \mathbb {Z} } d+1 = (P,1) ∩ Z {\displaystyle
Normal_polytope
Cryptography framework
represented as a binary vector over a normal basis in which each basis vector is the square of the preceding one. That is, the basis vectors are v1, v2, v4, v8,
Three-pass_protocol
Mathematical vector components
component of the vector, and another one perpendicular to the curve, called the normal component of the vector. Similarly, a vector at a point on a surface can
Tangential and normal components
Tangential_and_normal_components
1974 film by Mel Brooks
Normaali took their name from the movie. It is a translation of the name "Abby Normal" Igor uses to describe the abnormal brain he stole for the monster. List
Young_Frankenstein
Metabolically obese normal weight
Normal weight obesity or metabolically obese normal weight, also known as skinny fat, is the condition of having normal body weight, but with a high body
Normal_weight_obesity
Local coordinates that are adapted to a geodesic
orthonormal basis of T M {\displaystyle TM} with e 0 {\displaystyle e_{0}} parallel to γ ˙ {\displaystyle {\dot {\gamma }}} . Transport the basis { e a }
Fermi_coordinates
Vector satisfying some of the criteria of an eigenvector
complete basis for V {\displaystyle V} . This basis can be used to determine an "almost diagonal matrix" J {\displaystyle J} in Jordan normal form, similar
Generalized_eigenvector
Physical substance of the human organism
the cell via RNA. The RNA is then used to create proteins, which form the basis for cells, their activity, and their products. Proteins dictate cell function
Human_body
University in Nanchong, China
China West Normal University (CWNU; Chinese: 西华师范大学; pinyin: Xīhuá Shīfàn Dàxué) is a provincial public normal university featuring teachers education
China_West_Normal_University
Equivalence under a change of basis (linear algebra)
linear map under two possibly different bases, with P being the change-of-basis matrix. A transformation A ↦ P−1AP is called a similarity transformation
Matrix_similarity
Emblem of comic book superhero
original color, while changing shape here and there. The classic logo is the basis for virtually all other interpretations of the logo. In the mid-1990s, when
Superman_logo
Error in quantum-chemistry calculations due to overlapping basis sets
M. (2008). "Enthalpy difference between conformations of normal alkanes: Intramolecular basis set superposition error (BSSE) in the case of n-butane and
Basis_set_superposition_error
Association football tournament
period of great disruption. The championship was not played on a regular basis and many editions would be deemed unofficial, only to be considered valid
Copa_América
Penetrative sexual activity for reproduction or sexual pleasure
is in effect a substitute for intercourse and is often contrasted with 'normal intercourse' in this context. Reproductive methods also extend to gay and
Sexual_intercourse
Imperial unit of volumetric flow rate
Standard conditions for temperature and pressure). Normal cubic feet per minute (NCFM) refers to air at normal conditions, such as 14.7 psia, 68°F, 36% relative
Actual_cubic_feet_per_minute
Organ found in humans and other animals
atrioventricular node, and finally the ventricles (referred to as a normal sinus rhythm), this normal rhythm can be disrupted. Abnormal heart rhythms or arrhythmias
Heart
University in Jinhua, China
Zhejiang Normal University (ZJNU) is a public university in Jinhua city, Zhejiang province, China. Its main campus is next to the Shuanglong Cave national
Zhejiang_Normal_University
Perception of meaningful patterns or images in random or vague stimuli
messages in recorded music played in reverse or at higher- or lower-than-normal speeds, and hearing voices (mainly indistinct) or music in random noise
Pareidolia
Genital medical condition
single normal bladder and ureter. A 15-year-old boy, apart from having two penises, had normal external genitalia. His two testicles were within normal scrotum
Diphallia
Condition negatively affecting an organism
that impairs the normal functioning of the body. For this reason, diseases are associated with the dysfunction of the body's normal homeostatic processes
Disease
Legislature of Indian state
House, all the members are elected on the basis of adult franchise from single-seat constituencies. The normal tenure of the House is five years unless
Nagaland_Legislative_Assembly
Leader of China from 1949 to 1976
become a teacher and enrolled at the Fourth Normal School of Changsha, which soon merged with the First Normal School of Hunan, widely seen as the best in
Mao_Zedong
United States agency
and to maintain the property upon a reasonable basis." "The industry can be restored to a normal basis only by the introduction of economies in operation
Federal Electric Railways Commission
Federal_Electric_Railways_Commission
Flight maneuver
only gliders attempt such climbs on a regular basis. In some jurisdictions and under some conditions, normal climbs are defined by regulations or procedures
Climb_(aeronautics)
Creating multiple layers of protection against the propagation of failures or accidents
Defense-in-depth". Nrc.gov. 2012-12-26. Retrieved 2013-11-11. Daniel E Whitney (2003). "Normal Accidents by Charles Perrow" (PDF). Massachusetts Institute of Technology
Defense in depth (nuclear engineering)
Defense_in_depth_(nuclear_engineering)
Formalism to describe programming languages
Pāṇini–Backus Form (BNF or PBF, pronounced /ˌbækəs ˈnaʊər/), also known as Backus normal form, is a notation system for defining the syntax of programming languages
Backus–Naur_form
having particular shapes. Recent research has begun to explore the neural basis of these experiences, drawing both on neuroscientific principles and on
Neural_basis_of_synesthesia
Concepts from linear algebra
generalizes to the Jordan normal form. Over an algebraically closed field, any matrix A has a Jordan normal form and therefore admits a basis of generalized eigenvectors
Eigenvalues_and_eigenvectors
Result on cyclotomic fields, characterising those with a normal integral basis
theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of Q
Hilbert–Speiser_theorem
Cricket season review
not until 1946 that first-class cricket could resume in England on a normal basis. The West Indies were on tour and England won the Test series 1–0. The
1939_English_cricket_season
Rare disorder in which a person's lexicon is perceived as taste
cross-talk condition and how the findings may relate to neurologically normal persons. Tip of the tongue (TOT) studies refer to studies when higher order
Lexical–gustatory_synesthesia
Type of probability distribution
and it is a close approximation to the wrapped normal distribution, which, analogously to the linear normal distribution, is important because it is the
Circular_distribution
Kneecap, bone covering knee joint
X-ray of a normal adult right knee by anteroposterior projection. Patella is labeled in green lettering.
Patella
Metric on a smooth statistical manifold
metric is just ∇ θ 2 A {\displaystyle \nabla _{\theta }^{2}A} . Multivariate normal distribution N ( μ , Σ ) {\displaystyle {\mathcal {N}}(\mu ,\Sigma )} −
Fisher_information_metric
Categorisation of people's intelligence based on IQ
85 to 115, and about 5 percent of the population scores above 125 (i.e. normal distribution). When IQ testing was first created, Lewis Terman and other
IQ_classification
Genetic disorder which disrupts normal functioning of the olfactory and pituitary glands
functions normally at birth and well into adult life, giving normal puberty and normal reproductive function. The HPG axis then either fails totally
Kallmann_syndrome
Biological process of getting older
embryonic status and then used to grow a new tissue or animal without ageing. Normal human cells however die after about 50 cell divisions in laboratory culture
Ageing
Marked objects for finding random numbers
percentages, and summing the values of multiple dice produces approximations to normal distributions. "Uniform fair dice" are dice where all faces have an equal
Dice
Public normal university in Changchun, Jilin, China
Northeast Normal University (NENU; 东北师范大学) is a public normal university in Changchun, Jilin, China. It is affiliated with the Ministry of Education,
Northeast_Normal_University
Standardised contract to buy or sell an asset at a future date
mitigate the risk of default, the product is marked to market on a daily basis where the difference between the initial agreed-upon price and the actual
Futures_contract
Genetic disorder involving connective tissue
There is no known cure for MFS. Many of those with the disorder have a normal life expectancy with proper treatment. Management often includes the use
Marfan_syndrome
Prolonged period of excessively hot weather
area and to normal temperatures for the season. The main difficulties with this broad definition emerge when one must quantify what the 'normal' temperature
Heat_wave
Processes by which intelligence can change over time
Specifically, glutamatergic drugs may reduce the threshold for LTP, promote more normal dendritic spine morphology, and retain a greater number of useful synaptic
Malleability_of_intelligence
Canadian physician (born 1944)
Some commentators have raised concerns about the scope and evidentiary basis of his claims. Maté was born in Budapest, Hungary, in 1944 to a Jewish family
Gabor_Maté
External genitalia of the female mammal
hymen may also rupture spontaneously during exercise or be stretched by normal activities such as the use of tampons and menstrual cups, or be so minor
Vulva
Marriage in Poland may be performed as a civil or religious ceremony. The normal legal minimum age to marry is 18, however, women 16 or older may seek family
Marriage_in_Poland
Hypothesized anatomical detail
experience G-spot stimulation, and emphasize that not experiencing it is normal. Two primary methods have been used to define and locate the G-spot as a
G-spot
Boolean polynomials as sums of monomials
Algebraic normal form (ANF) is a representation of functions in boolean algebra. Formulas written in ANF are also known as ring sum normal form (RSNF or
Algebraic_normal_form
Method for estimating the unknown parameters in a linear regression model
which implies that the response variable itself has a log-normal distribution rather than a normal distribution). Uncorrelatedness of errors. This assumes
Ordinary_least_squares
NORMAL BASIS
NORMAL BASIS
Boy/Male
Biblical
Treasurer of Nergal.
Girl/Female
Indian
Soft
Girl/Female
American, Australian, British, Chinese, Christian, Danish, English, Finnish, French, German, Latin, Swedish
From the North; Pattern; Courage; Norseman; Rule; Standard; Female Version of Norman
Female
English
English name derived from the gem name, from Latin corallium, probably ultimately from Hebrew goral, CORAL means "small pebble."
Boy/Male
American, Australian, French, Scottish
From the Northern Town
Boy/Male
Afghan, Arabic
Handsome
Female
Italian
 Italian name invented by Felice Romani in his libretto for Belini's opera of the same name, derived from Latin norma, NORMA means "standard, rule." Compare with another form of Norma.
Boy/Male
French Teutonic American English German
From the north.
Boy/Male
Assamese, Bengali, Celebrity, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Punjabi, Sikh, Sindhi, Tamil, Telugu, Traditional
Kindness; Clean; Pure; Talent Person; The One who is Pure
Girl/Female
Latin American
Rule; pattern. Can also be a feminine form of Norman: from the North.
Male
English
English form of Teutonic Nordemann, NORMAN means "northman."
Boy/Male
Hindu
Clean, Pure
Boy/Male
Scottish American
From the north valley.
Female
English
 Feminine form of English Norman, NORMA means "northman." Compare with another form of Norma.
Male
Scottish
Scottish form of Irish Gaelic Cormac, CORMAG means "son of defilement."
Girl/Female
Indian, Punjabi, Sikh, Telugu
Pure; Without Any Impurity
Surname or Lastname
English, Irish (Ulster), Scottish, and Dutch
English, Irish (Ulster), Scottish, and Dutch : name applied either to a Scandinavian or to someone from Normandy in northern France. The Scandinavian adventurers of the Dark Ages called themselves norðmenn ‘men from the North’. Before 1066, Scandinavian settlers in England were already fairly readily absorbed, and Northman and Normann came to be used as bynames and later as personal names, even among the Saxon inhabitants. The term gained a new use from 1066 onwards, when England was settled by invaders from Normandy, who were likewise of Scandinavian origin but by now largely integrated with the native population and speaking a Romance language, retaining only their original Germanic name.French : regional name for someone from Normandy.Dutch : ethnic name for a Norwegian.Jewish (Ashkenazic) : variant of Nordman.Jewish : Americanized form of some like-sounding Ashkenazic name.Swedish : from norr ‘north’ + man ‘man’.Albert Andriessen Bradt, a settler in Rensselaerswijck on the upper Hudson River in NY, was originally from Norway and was known as de Norrman (‘the Norwegian’). The waterway south of Albany which powered his mills became known as the Normanskill (‘the Norman’s Waterway’), by which name it is still known today.
Boy/Male
Shakespearean
Hamlet, Prince of Denmark' Fortinbras, Prince of Norway.
Biblical
treasurer of Nergal
Male
English
English form of Norwegian Normund, NORMAND means "north protection."
NORMAL BASIS
NORMAL BASIS
Girl/Female
Tamil
Strange
Surname or Lastname
English
English : variant spelling of Moulton.
Boy/Male
Hawaiian American
The free one.
Girl/Female
American, Australian, Christian, Danish, Finnish, German, Greek, Latin, Swedish
Roman Goddess of the Hearth; Fireside
Girl/Female
English American French
meaning favor; grace.
Surname or Lastname
English and Dutch
English and Dutch : patronymic from Wilkin.
Boy/Male
German
The eagle rules; strong as an eagle. Famous Bearer: Movie star and producer/directer Arnold...
Girl/Female
Australian, French, German, Hebrew, Swedish
Pledged to God; My God is a Vow; God is My Oath
Girl/Female
Australian, Dutch, German
Noble
Boy/Male
Indian, Sanskrit
Irresistable; Unconquerable
NORMAL BASIS
NORMAL BASIS
NORMAL BASIS
NORMAL BASIS
NORMAL BASIS
a.
Serving to teach or convey a moral; as, a moral lesson; moral tales.
a.
According to a square or rule; perpendicular; forming a right angle. Specifically: Of or pertaining to a normal.
adv.
In a normal manner.
n.
See Mormal.
n.
See Wormil.
a.
Having the form or appearance without the substance or essence; external; as, formal duty; formal worship; formal courtesy, etc.
a.
According to an established norm, rule, or principle; conformed to a type, standard, or regular form; performing the proper functions; not abnormal; regular; natural; analogical.
a.
Alt. of Loral
a.
Sound; normal.
a.
Not according to rule; abnormal.
a.
Denoting certain hypothetical compounds, as acids from which the real acids are obtained by dehydration; thus, normal sulphuric acid and normal nitric acid are respectively S(OH)6, and N(OH)5.
n.
The quality, state, or fact of being normal; as, the point of normalcy.
a.
Both renal and portal. See Portal.
a.
Denoting that series of hydrocarbons in which no carbon atom is united with more than two other carbon atoms; as, normal pentane, hexane, etc. Cf. Iso-.
a.
Pertaining to, or situated near, the back, or dorsum, of an animal or of one of its parts; notal; tergal; neural; as, the dorsal fin of a fish; the dorsal artery of the tongue; -- opposed to ventral.
n.
See Wormil.
a.
Done in due form, or with solemnity; according to regular method; not incidental, sudden or irregular; express; as, he gave his formal consent.
a.
Of or pertaining to Normandy or to the Normans; as, the Norman language; the Norman conquest.
a.
Northern; pertaining to the north, or to the north wind; as, a boreal bird; a boreal blast.
a.
Human; belonging to man, who is mortal; as, mortal wit or knowledge; mortal power.