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Diagonalization is the process of re-ordering the rows and columns of tables and charts so that the data forms an approximately diagonal line. This makes
Table_diagonalization
Topics referred to by the same term
Look up diagonalization in Wiktionary, the free dictionary. In logic and mathematics, diagonalization may refer to: Matrix diagonalization, a construction
Diagonalization
Tabular arrangement of the chemical elements
chemical characteristics. Vertical, horizontal and diagonal trends characterize the periodic table. Metallic character increases going down a group and
Periodic_table
Groups of stars in Ancient Egyptian astronomy
surrounding the observation methods used to develop and populate the diagonal star tables, and the criteria used to select decans (brightness, position, relationship
Decan
Proof in set theory
incompleteness theorems and Turing's answer to the Entscheidungsproblem. Diagonalization arguments are often also the source of contradictions like Russell's
Cantor's_diagonal_argument
Table that displays the frequency of variables
In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the multivariate
Contingency_table
Mathematical table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for
Multiplication_table
Graph of neutrons vs. protons in nuclides
neighbor each other diagonally from lower-left to upper-right. Examples include carbon-14, nitrogen-14, and oxygen-14 in the table above. Isodiaphers are
Table_of_nuclides
Mathematical table used in logic
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which
Truth_table
Relationship between elements on the periodic table
In chemistry, a diagonal relationship is said to exist between certain pairs of diagonally adjacent elements in the second and third periods (first 20
Diagonal_relationship
Table layout for visualizing performance; also called an error matrix
the diagonal of the table (highlighted in green), so it is easy to visually inspect the table for prediction errors, as values outside the diagonal will
Confusion_matrix
1617 device for calculating products and quotients
into two halves by a diagonal line from the bottom left corner to the top right. The squares contain a simple multiplication table. The first holds a single
Napier's_bones
Different forms of the table of elements
published an associated periodic table of chemical elements, authors have experimented with varying types of periodic tables for teaching, aesthetic or philosophical
Types_of_periodic_tables
Term in options trading
We can obtain a third view of the long box-spread by reading the table diagonally. A long box-spread can be viewed as a long strangle at one pair of
Box_spread
Mathematical tool in group theory
Cayley table and a zero in every other position, the Kronecker delta function for that symbol. (Note that e is in every position down the main diagonal, which
Cayley_table
Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle
Ptolemaeus). Ptolemy used the theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy. If the vertices of the cyclic
Ptolemy's_theorem
Method of visualizing the relationship between elements
A period on the periodic table is a row of chemical elements. All elements in a row have the same number of electron shells. Each next element in a period
Period_(periodic_table)
Flat tool used in carpentry to mark right angles and calculate angles
stringers. There is a table of numbers on the face side of the steel square; this is called the rafter table. The rafter table allows the carpenter to
Steel_square
Babylonian clay tablet of numbers in Pythagorean triples
written around 1800 BC, that contains a mathematical table written in cuneiform script. Each row of the table relates to a Pythagorean triple, that is, a triple
Plimpton_322
Computation model defining an abstract machine
abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing
Turing_machine
Key layout for musical instruments
The Harmonic Table note-layout, or tonal array, is a key layout for musical instruments that offers interesting advantages over the traditional keyboard
Harmonic_table_note_layout
Machine learning framework for portfolio construction
concentrated along the diagonal. This process is referred to as a quasi-diagonalization of the covariance matrix. Unlike full diagonalization, this method does
Hierarchical_Risk_Parity
Clothing and fashion trends of the Byzantine Empire
Ravenna mosaics. On each straight edge men of the senatorial class had a tablion, a lozenge shaped coloured panel across the chest or midriff (at the front)
Byzantine_dress
Directional planes
plumbline verticality but for the student the axis may well lie on a horizontal table. Although the word horizontal is commonly used in daily life and language
Vertical_and_horizontal
contract based on a Moysian fit. Screen A device which divides the table diagonally, visually separating partners from each other. Used in higher-level
Glossary of contract bridge terms
Glossary_of_contract_bridge_terms
Estimates values in an N-dimensional matrix
close to u and v. Notes: For the RAS form of the algorithm, define the diagonalization operator d i a g : R k ⟶ R k × k {\displaystyle diag:\mathbb {R} ^{k}\longrightarrow
Iterative proportional fitting
Iterative_proportional_fitting
Logical connective AND
set of operands) is often defined as having the result true. The truth table of A ∧ B {\displaystyle A\land B} : In systems where logical conjunction
Logical_conjunction
Men's national soccer team representing United States
States v Bosnia and Herzegovina United States v Belgium The following table shows the United States all-time international record, correct as of July
United States men's national soccer team
United_States_men's_national_soccer_team
Hash collision resolution technique
addressing, or closed hashing, is a method of collision resolution in hash tables. With this method a hash collision is resolved by probing, or searching
Open_addressing
Limitative results in mathematical logic
This is done using a technique called "diagonalization" (so-called because of its origins as Cantor's diagonal argument). Within the formal system this
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Mathematical transform that expresses a function of time as a function of frequency
compact, and it preserves the orthonormality of the character table. Each row of the table is the function e k ( x ) {\displaystyle e_{k}(x)} of x ∈ T
Fourier_transform
Printed lists of randomly created digits
method correctly. Tables of random numbers have the desired properties no matter how chosen from the table: by row, column, diagonal or irregularly. The
Random_number_table
2nd century AD trigonometric table
The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in
Ptolemy's_table_of_chords
Association football club in England
Manchester Stadium. The first four seasons at the stadium all resulted in mid-table finishes. Former England manager Sven-Göran Eriksson became the club's first
Manchester_City_F.C.
Trapezoid symmetrical about an axis
legs and both base angles are of equal measure, or as a trapezoid whose diagonals have equal length. Note that a non-rectangular parallelogram is not an
Isosceles_trapezoid
Physical size of pictures and videos
visual field. Common screen dimensions are listed in the table below (the most common diagonal dimensions in inches as of 2020 are bolded). If the display
Display_size
Philosophical system based on the teachings of Pythagoras
extended to all the opposites, which descent from the so-called Pythagorean "Table of ten Opposites", mentioned by Aristotle. Supreme opposites are the following
Pythagoreanism
Cricket Tournament
Scotland won the toss and elected to bat. Teams will face each other in diagonal form in Super 6, which means A1 will face D2 and D3, A2 will face D1 and
2026 Under-19 Men's Cricket World Cup
2026_Under-19_Men's_Cricket_World_Cup
Chemical element with atomic number 5 (B)
neutron-capturing agent. Borates have low toxicity in mammals (similar to table salt) but are more toxic to arthropods and are occasionally used as insecticides
Boron
National Hockey League season
feature a lighter shade of blue compared to their regular jerseys and the diagonal "RANGERS" wordmark in white lettering, paying tribute to the uniforms worn
2025–26_NHL_season
Strategy board game
jumps made by a single piece; the jumps do not need to be on the same diagonal direction and may "zigzag" (change direction). In American checkers and
Checkers
Italian football manager (born 1959)
FA Community Shield in August, Ancelotti led Chelsea to the top of the table on the first weekend of the season thanks to a 6–0 rout of newly promoted
Carlo_Ancelotti
ball after each other. Crosscourt When a player hits the ball diagonally across the table. Crossover The point where a player has to change from playing
Glossary_of_table_tennis
half black U+25E9 ◩ Square with upper left diagonal half black U+25EA ◪ Square with lower right diagonal half black U+25EB ◫ White square with vertical
List_of_Unicode_characters
Cuboid whose edges and face diagonals have integer lengths
named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose
Euler_brick
Indication of topological symmetry groups to topological condensed matter
Bott clock (see below) so that the same values repeat in the diagonals. An X in the table of "Symmetries" indicates that the symmetry of the Hamiltonian
Periodic table of topological insulators and topological superconductors
Periodic_table_of_topological_insulators_and_topological_superconductors
Array in complex analysis
In complex analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants Rm, n to a given complex formal power series
Padé_table
Federal capital district of the United States
A01. Archived from the original on May 4, 2011. Retrieved July 25, 2008. "Table 15. Number of private schools, students, full-time equivalent (FTE) teachers
Washington,_D.C.
Database of precalculated chess analysis
consists of two tables per endgame: a smaller WDL (win/draw/loss) table which contains knowledge of the 50-move rule, and a larger DTZ table (distance to
Endgame_tablebase
Small domesticated carnivorous mammal
Spofford, N.; C., H.; Hours, M.-A.; Biourge, V. (2023). "Life expectancy tables for dogs and cats derived from clinical data". Frontiers in Veterinary Science
Cat
Card game
competing partnerships, with partners sitting opposite each other around a table. The game consists of a number of deals, each progressing through four phases
Contract_bridge
ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set. Explanations of the symbols
List of mathematical constants
List_of_mathematical_constants
Study of gas-vapor mixtures
vertical axis of the chart. Specific enthalpy: These are oblique lines drawn diagonally downward from left to right across the chart that are parallel to each
Psychrometrics
Chemical element with atomic number 3 (Li)
energy per nucleon (compared to the neighboring elements on the periodic table, helium and beryllium); lithium is the only low numbered element that can
Lithium
2025 smartphone by Apple
line's LCD. The display has a resolution of 2532 × 1170 pixels, with a diagonal size of 6.1 in (150 mm) and a pixel density of 460 PPI. It can play HDR10
IPhone_16e
Painting by Matthias Stom
tenebrist manner, the canvas reveals Saint Jerome seated at a solitary table, enveloped by shadow. Before him lie the emblems of devotion and mortality:
Saint_Jerome_(Stom)
ISBN 9780060589929 – via Google Books. Schwartz, Arthur (October 7, 1998). Naples at Table: Cooking in Campania. Harper Collins. ISBN 9780060182618 – via Google Books
List_of_pasta
Chinese stealth fighter aircraft
made their maiden debut as part of the PLAAF arsenal. The following is a table of significant milestones in the J-20 program history as gleaned from public
Chengdu_J-20
Four-sided polygon
In the following table it is listed if the diagonals in some of the most basic quadrilaterals bisect each other, if their diagonals are perpendicular
Quadrilateral
National Hockey League season
black, and salt white. The home uniforms consisted of a black base with a diagonal "UTAH" wordmark across the front, with blue and white striping, with the
2024–25_NHL_season
Bridge in New York City
elements of cable-stayed and suspension bridges, with both vertical and diagonal suspender cables. Its stone towers are neo-Gothic, with characteristic
Brooklyn_Bridge
American comedian (1953–1992)
reportedly stated as he was staring at something or someone, while in a diagonal position, leaning on the middle console. His brother told him, “some help
Sam_Kinison
Group of symmetries of the square
not commutative, which can be seen from the table; the table is not symmetrical about the main diagonal. There are five different groups of order 8.
Dihedral_group_of_order_8
Non-singular cubic surface in mathematics
In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by Clebsch (1871) and
Clebsch_surface
Small plate
individual table setting. If a butter spreader is used, it is laid on top of the B&B plate, either vertically, horizontally, or diagonally. The modern
Bread-and-butter_plate
Triangular array of the binomial coefficients
Raymond de Montmort (1708) who called it table de M. Pascal pour les combinaisons (French: Mr. Pascal's table for combinations) and Abraham de Moivre (1730)
Pascal's_triangle
Chemical element with atomic number 7 (N)
Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated
Nitrogen
Letter of the Latin alphabet; used in the German language
(1998-04-15). "cp1250 to Unicode table". Microsoft / Unicode Consortium. Steele, Shawn (1998-04-15). "cp1252 to Unicode table". Microsoft / Unicode Consortium
ß
Mathematical function, inverse of an exponential function
computations more easily. Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition. This is
Logarithm
Mathematical statistics distance measure
Kullback gives the following example (Table 2.1, Example 2.1). Let P and Q be the distributions shown in the table and figure. P is the distribution on
Kullback–Leibler_divergence
Polygon shape with eight sides
types of diagonals: Short diagonal; Medium diagonal (also called span or height), which is twice the length of the inradius; Long diagonal, which is
Octagon
Typographical mark (\)
using the Wheatstone system. In a 1945 document, Teletype used the name "diagonal key" for the symbol, and gives it a (non-standard) Morse code of ▄ ▄▄▄ ▄ ▄ ▄▄▄
Backslash
Primary time standard globally used to regulate clocks and time
exact time interval elapsed between two UTC timestamps without consulting a table showing how many leap seconds occurred during that interval. By extension
Coordinated_Universal_Time
Babylonian mathematical clay tablet
tablet YBC 7243. The constant appears on line 10 of the table along with the inscription, "the diagonal of a square". The mathematical significance of this
YBC_7289
Base-16 numeric representation
062510 (one-sixteenth) is equivalent to 0.116, 0.0912, and 0;3,4560. The table below gives the expansions of some common irrational numbers in decimal
Hexadecimal
Method of deriving conclusions
that an argument is valid. Alternative methods include the use of truth tables, which apply to propositional logic, and truth trees, which can also be
Rule_of_inference
Triangle of numbers
element missing in the case of the rightmost diagonal). The next diagonal parallel to the rightmost diagonal gives the sequence of differences of two consecutive
Bell_triangle
Technical drawing instrument
draftsmen primarily as a guide for drawing horizontal lines on a drafting table. The instrument is named after its resemblance to the letter T, with a long
T-square
Matrix in which most of the elements are zero
linear algebra support ARPACK Fortran 77 library for sparse matrix diagonalization and manipulation, using the Arnoldi algorithm SLEPc Library for solution
Sparse_matrix
Spanish professional football club
finishing in the top half of the table in 16 out of 19 seasons, and are ranked 12th in the all-time La Liga table. As a result, the club was a regular
Deportivo_de_A_Coruña
Diagonal intersection is a term used in mathematics, especially in set theory. If δ {\displaystyle \displaystyle \delta } is an ordinal number and ⟨ X
Diagonal_intersection
Matrix with the same number of rows and columns
The entries a i i {\displaystyle a_{ii}} (i = 1, ..., n) form the main diagonal of a square matrix. They lie on the imaginary line which runs from the
Square_matrix
Standards defined by VESA for mounting flat panel displays to stands or wall mounts
seen from the tables below. Notes If a screen is heavier or larger than specified in table 1, it should use a larger variant from the table, for instance
VESA_mount
Four-dimensional number system
multiplication table of unit quaternions. For example, the last matrix representation given above corresponds to the multiplication table which is isomorphic
Quaternion
Chemical element with metallic and nonmetallic properties
selenium, polonium and astatine. On a standard periodic table, all eleven elements are in a diagonal region of the p-block extending from boron at the upper
Metalloid
Group of highly reactive chemical elements
hydrogen they constitute group 1, which lies in the s-block of the periodic table. All alkali metals have their outermost electron in an s-orbital: this shared
Alkali_metal
Statistical model for a binary dependent variable
(cardinal numbers), then simple regression analysis could be used. The table shows the number of hours each student spent studying, and whether they
Logistic_regression
Elementary particle involved with rest mass
Cross Sections: 2. Differential Distributions (Report). CERN Report 2 (Tables A.1–A.20). Vol. 1201. p. 3084. arXiv:1201.3084. Bibcode:2012arXiv1201.3084L
Higgs_boson
Eighteenth letter of the latin alphabet
language. ⟨R⟩ represents a rhotic consonant in many languages, as shown in the table below. Other languages may use the letter ⟨r⟩ in their alphabets (or Latin
R
1972 novel by Italo Calvino
while moving down the list, in a rigorous mathematical structure. The table below lists the cities in order of appearance, along with the group they
Invisible_Cities
Horizontal support element of an item of furniture
connecting the legs diagonally, frequently with a finial where the stretchers crossed. Gateleg table Hayrake table Refectory table Palisander chair Trestle
Stretcher_(furniture)
Statistical technique
in a biplot any structure hidden in the multivariate setting of the data table. As such it is a technique from the field of multivariate ordination. Since
Correspondence_analysis
Chinese tile-based game
slightly diagonal position (about 20 to 30 degrees counter-clockwise); the right end of their stack is pushed somewhat further into the centre of the table to
Mahjong
Association football club in Brazil
Santos was able to surpass Atlético Paranaense, who had been on top of the table for the majority of the season. In the last match Santos did not crumble
Santos_FC
Convex quadrilateral with at least one pair of parallel sides
angle between a side and a diagonal is equal to the angle between the opposite side and the same diagonal. The diagonals cut each other in mutually the
Trapezoid
Cricket Tournament
December 2023 – via X (formerly Twitter). "ICC UNDER-19 WORLD CUP POINTS TABLE". ESPNcricinfo. Retrieved 26 January 2024. "ICC reveals U19 Men's Cricket
2024 Under-19 Cricket World Cup
2024_Under-19_Cricket_World_Cup
Ratio between a display's width and height
as the diagonal measurement of its display area, usually in inches. Wider aspect ratios result in smaller overall area, given the same diagonal. Most televisions
Display_aspect_ratio
Any of a set of standard configurations of Redundant Arrays of Independent Disks
full performance penalty of RAID 6 is seen during writes. The following table provides an overview of some considerations for standard RAID levels. In
Standard_RAID_levels
Board game
been common knowledge in the context the book originated in. In Board and Table Games from Many Civilizations, R. C. Bell writes that "when the Moors invaded
Alquerque
Platformer video game
of 1982. Game Machine later listed the game as the 20th most successful table arcade cabinet of September 1983. In the United States, Donkey Kong topped
Donkey_Kong_(1981_video_game)
TABLE DIAGONALIZATION
TABLE DIAGONALIZATION
Surname or Lastname
English
English : from the female personal name (A)mabel (see Mabbitt).
Girl/Female
Arabic, Muslim
Associate; Table Companion
Boy/Male
Biblical
A moist table.
Girl/Female
English American Latin
Lovable.
Boy/Male
Arabic
Table Companion; Associate
Girl/Female
African, Egyptian, German
Green
Boy/Male
English
Ropemaker. An English surname.
Female
English
English name derived from the vocabulary word, SABLE means "black," as a heraldic color. It is sometimes confused with the mammal of the same name but which has brown fur, not black, and which has a different origin.
Surname or Lastname
English
English : variant spelling of Abel. Probably also an Americanized spelling of the same surname in other languages.
Boy/Male
Muslim
Table companion. Associate.
Female
English
Variant spelling of English Mabel, MABLE means "lovable."Â
Boy/Male
American, Australian, British, English
Rope; Rope-maker; An English Surname
Male
English
English surname transferred to forename use, possibly originally a habitational name derived from a place named from Old Norse gafl, GABLE means "gable," a term used to denote a "triangular-shaped hill."Â
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : occupational name from Old French tablier ‘joiner’.
Girl/Female
Biblical
A table, news.
Girl/Female
American, Australian, British, Christian, English, Latin
Lovable; Diminutive of Amabel; Worthy of Being Loved
Girl/Female
American, Australian, British, Chinese, Christian, English
Black
Surname or Lastname
English
English : metonymic occupational name for a maker of rope, especially the type of stout rope used in maritime applications, from Anglo-Norman French cable ‘cable’ (Late Latin capulum ‘halter’, of Arabic origin, but associated by folk etymology with Latin capere ‘to seize’).English : possibly from an Old English personal name, Ceadbeald.English : metonymic occupational name for a horseman, from Middle English cabal ‘horse’.From German Göbel (see Goebel), assimilated to the English name.
Boy/Male
Hebrew
Exhalation of breath. The second son of Adam in the bible. The variant Able is used as an English...
Male
English
Variant spelling of English Abel, ABLE means "vanity," i.e. "transitory."
TABLE DIAGONALIZATION
TABLE DIAGONALIZATION
Girl/Female
Arabic, Muslim
Wine Cup
Girl/Female
Muslim
A narrator of Hadith
Boy/Male
Scottish Irish
From the craggy hills.' Tor is a name for a craggy hilltop and also may refer to a watchtower.
Boy/Male
Tamil
Dimple of cheeks
Surname or Lastname
English
English : variant of Crossland.
Girl/Female
Arabic, Australian
Heaven Gates; Pure Water
Boy/Male
Arabic
Supporter of the Faith
Boy/Male
Irish
Fair birth; handsome.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Moon
Girl/Female
Indian
I am, Self-confident
TABLE DIAGONALIZATION
TABLE DIAGONALIZATION
TABLE DIAGONALIZATION
TABLE DIAGONALIZATION
TABLE DIAGONALIZATION
n.
Any collection and arrangement in a condensed form of many particulars or values, for ready reference, as of weights, measures, currency, specific gravities, etc.; also, a series of numbers following some law, and expressing particular values corresponding to certain other numbers on which they depend, and by means of which they are taken out for use in computations; as, tables of logarithms, sines, tangents, squares, cubes, etc.; annuity tables; interest tables; astronomical tables, etc.
n.
The fur of the sable.
v. t.
To form into a table or tables; to reduce to tables or synopses.
n.
A small table or flat surface.
n.
The company assembled round a table.
v. t.
To lay or place on a table, as money.
v. t.
To fasten with a cable.
n.
A table; a tablet.
v. t.
To delineate, as on a table; to represent, as in a picture.
v. i.
Durable; not subject to overthrow or change; firm; as, a stable foundation; a stable position.
pl.
of Table d'hote
v. t.
To enter upon the docket; as, to table charges against some one.
n.
A cable.
v. t. & i.
To telegraph by a submarine cable
n.
Hence, food placed on a table to be partaken of; fare; entertainment; as, to set a good table.
v. t.
To form into a table or catalogue; to tabulate; as, to table fines.
v. t.
To put or keep in a stable.
n.
One of the divisions of a backgammon board; as, to play into the right-hand table.
v. i.
To live at the table of another; to board; to eat.