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In algebra, a generic matrix ring is a sort of a universal matrix ring. We denote by F n {\displaystyle F_{n}} a generic matrix ring of size n with variables
Generic_matrix_ring
Mathematical ring whose elements are matrices
abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set
Matrix_ring
Array of numbers
n-by-n matrices over R is a ring called matrix ring, isomorphic to the endomorphism ring of the left R-module Rn. If the ring R is commutative, that is
Matrix_(mathematics)
For a square matrix, the transpose of the cofactor matrix
commutative ring and A is an n × n matrix with entries from R. The (i, j)-minor of A, denoted Mij, is the determinant of the (n − 1) × (n − 1) matrix that results
Adjugate_matrix
1999 film by the Wachowskis
The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. The first installment in the Matrix film series, it stars Keanu
The_Matrix
Ring that is also a vector space or a module
derived algebraic geometry. See also: Generic matrix ring. A homomorphism between two R-algebras is an R-linear ring homomorphism. Explicitly, φ : A1 → A2
Associative_algebra
{\displaystyle (xy-yx)^{2}=-\det(xy-yx)I} for any 2-by-2-matrices x and y. Generic matrix ring Formanek, Edward (1991). The polynomial identities and invariants
Central_polynomial
Mathematical concept in polynomial theory
polynomials over a field or over a commutative ring is commonly defined as the determinant of their Sylvester matrix. More precisely, let A = a 0 x d + a 1 x
Resultant
Algebraic structure with addition and multiplication
operations. For n = 1, this matrix ring is isomorphic to R itself. For n > 1 (and R not the zero ring), this matrix ring is noncommutative. If G is an
Ring_(mathematics)
1998 Japanese horror film by Hideo Nakata
the year, beating popular American films such as The Matrix. On its 1999 Hong Kong release, Ring earned HK$31.2 million (US$4.03 million) during its two-month
Ring_(film)
Square matrices satisfy their characteristic equation
Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies
Cayley–Hamilton_theorem
bracket ring is the subring of the ring of polynomials k[x11,...,xdn] generated by the d-by-d minors of a generic d-by-n matrix (xij). The bracket ring may
Bracket_ring
In mathematics, invariant of square matrices
square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the
Determinant
Concept in algebraic geometry
ring k[x1,..., xn]. The affine scheme X is smooth of dimension m over k if X has dimension at least m in a neighborhood of each point, and the matrix
Smooth_scheme
Every ring is (isomorphic to) the full matrix ring over itself. 2. The ring of generic matrices is the ring consisting of square matrices with entries
Glossary_of_ring_theory
Four-dimensional number system
of one CSA being a matrix ring over another. By the Artin–Wedderburn theorem (specifically, Wedderburn's part), CSAs are all matrix algebras over a division
Quaternion
States that the algebra of n by n matrices satisfies a certain identity of degree 2n
a commutative ring satisfies a certain identity of degree 2n. It was proved by Amitsur and Levitsky (1950). In particular matrix rings are polynomial
Amitsur–Levitzki_theorem
Elementwise product of two matrices
a matrix of the multiplied corresponding elements. This operation can be thought as a "naive matrix multiplication" and is different from the matrix product
Hadamard_product_(matrices)
Set of a ring's prime ideals
commutative ring is naturally endowed with a sheaf of commutative rings, called the structure sheaf, which makes it a ringed space; that is, commutative rings are
Spectrum_of_a_ring
Mountain in United States of America
the sandstones and the serpentinite-matrix melange is not exposed. Landslides and their deposits are abundant on Ring Mountain, for example at Triangle
Ring_Mountain_(California)
Type of commutative ring in mathematics
determinantal ring. That is, let R be the quotient of a regular local ring S by the ideal I generated by the r × r minors of some p × q matrix of elements
Cohen–Macaulay_ring
Deformation of the group algebra of a Coxeter group
following data: (W, S) is a Coxeter system with the Coxeter matrix M = (mst), R is a commutative ring with identity, {qs | s ∈ S} is a family of units of R
Iwahori–Hecke_algebra
Term in algebraic geometry
Noting that Spec K is the generic point of Spec R and discrete valuation rings are precisely the regular local one-dimensional rings, one may rephrase the
Proper_morphism
Initiatives to enhance the performance of firms in external environments
management consulting industry. Completion of an importance-performance matrix forms "a crucial stage in the formulation of operations strategy", and may
Strategic_management
\left({\begin{matrix}x&y&z\\x_{1}&y_{1}&z_{1}\\x_{2}&y_{2}&z_{2}\end{matrix}}\right)\left({\begin{matrix}a\\b\\c\end{matrix}}\right)=\left({\begin{matrix
Incidence_(geometry)
Submodule of a mathematical ring
simple commutative ring is a field. The matrix ring over a skew-field is a simple ring. If f : R → S {\displaystyle f:R\to S} is a ring homomorphism, then
Ideal_(ring_theory)
Programming language for statistics
12 20 30 42 > z_matrix <- matrix(z, nrow = 3) # Create a new matrix that transforms the # vector z into a 3x2 matrix object > z_matrix [,1] [,2] [1,] 2
R_(programming_language)
Israeli mathematician (1921–1994)
of polynomial identities of matrix algebras. His work on the embedding of PI-rings into matrix rings over commutative rings, and his results on noncommutative
Shimshon_Amitsur
Class of synthetic fiber related to nylon
accepted in 1974 by the Federal Trade Commission of the USA as the name of a generic category of fiber distinct from nylon, and adopted by the International
Aramid
Branch of algebraic geometry
a vector space, which is roughly equivalent to describing the cohomology ring of Grassmannians. Sometimes it is used to mean the more general enumerative
Schubert_calculus
Optical machine-readable representation of data
developed, using rectangles, dots, hexagons and other patterns, called matrix codes or 2D barcodes. Despite being often included as barcodes, these do
Barcode
linear algebra theorems. An n by m matrix M with entries Mij over a ring R (not necessarily commutative) is a Manin matrix if all elements in a given column
Manin_matrix
Function of the coefficients of a polynomial that gives information on its roots
numbers (i.e. injective ring homomorphisms K → C). The discriminant of K is the square of the determinant of the n by n matrix B whose (i,j)-entry is σi(bj)
Discriminant
Matrix decomposition in mathematics
entries that are polynomials in z − 1 {\displaystyle z^{-1}} . For a generic matrix we have M 0 = i d {\displaystyle M^{0}=\mathrm {id} } . Birkhoff factorization
Birkhoff_factorization
Cryptography secured against quantum computers
such as learning with errors, ring learning with errors (ring-LWE), the ring learning with errors key exchange and the ring learning with errors signature
Post-quantum_cryptography
Analogs of homology groups for algebraic varieties
ring homomorphism from the Chow ring to the cohomology ring. Intuitively, this is because the products in both the Chow ring and the cohomology ring describe
Chow_group
Greatest common divisor of polynomials
resultant of P and Q is the determinant of the Sylvester matrix, which is the (square) matrix of φ 0 {\displaystyle \varphi _{0}} on the bases of the powers
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Algebraic variety defined within an affine space
prime, non-maximal ideals of the coordinate ring). This creates a more well-defined notion of the "generic point" of an affine variety, by assigning to
Affine_variety
Special type of aromaticity
matrix the resonance integral between carbon 1 {\displaystyle 1} and N {\displaystyle N} is − β ′ {\displaystyle -\beta ^{\prime }} . For the generic
Möbius_aromaticity
condition that a matrix have rank ≤ r is given by the vanishing of all of its (r + 1) × (r + 1) minors. Considering the generic m × n matrix whose entries
Determinantal_variety
Standardized protocol
SDH or SONET as communications protocols in and of themselves; they are generic, all-purpose transport containers for moving both voice and data. The basic
Synchronous optical networking
Synchronous_optical_networking
-x+x^{2}-\dotsb +(-x)^{n}} ). In the second convention, a matrix is quasiregular in a matrix ring if it does not possess −1 as an eigenvalue. More generally
Quasiregular_element
Theorem in algebraic geometry
\ldots ,\varphi (f_{n}).} This ideal is also generically a prime ideal, as it is prime if R is the ring of integer polynomials with the all coefficients
Main theorem of elimination theory
Main_theorem_of_elimination_theory
Fluoroquinolone antibiotic
ciprofloxacin as critically important for human medicine. It is available as a generic medication. In 2023, it was the 155th most commonly prescribed medication
Ciprofloxacin
Antibiotic
Organization's List of Essential Medicines. Tetracycline is available as a generic medication. Tetracycline was originally made from bacteria of the genus
Tetracycline
Genus of tapejarid pterosaur
new genus and species Europejara olcadesorum was named based on it. The generic name refers to Europe, where it was found, and to the related genus Tapejara
Europejara
Polycyclic organic compound having sterane as a core structure
fused rings: three six-member cyclohexane rings (rings A, B and C in the first illustration) and one five-member cyclopentane ring (the D ring). Steroids
Steroid
a now lost Indo-Iranian form. In Pliny’s Natural History, iaspis is a generic term that encompasses fourteen types of gemstones. This makes it difficult
Gemstones_in_the_Bible
Curve from a cone intersecting a plane
matrix}A&B/2&D/2\\B/2&C&E/2\\D/2&E/2&F\end{matrix}}\right)\left({\begin{matrix}x\\y\\z\end{matrix}}\right)=0.} The 3 × 3 matrix above is called
Conic_section
1949, p.16) 4. Local rings are integrally closed; see normal scheme. null-polarity A correlation given by a skew symmetric matrix. A null-polarity of the
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
Sheaf consisting of modules on a ringed space; generalizing vector bundles
In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf of abelian groups F such that, for any open subset U of
Sheaf_of_modules
Games for the Sony PlayStation / PS1 / PSone
PlayStation game released in Japan (not counting re-releases) was Black/Matrix 00 on May 13, 2004; counting re-releases, the final licensed game released
List of PlayStation (console) games (A–L)
List_of_PlayStation_(console)_games_(A–L)
Genus of trees known as baobab
oval to round and berry-like, and hold kidney-shaped seeds in a dry, pulpy matrix. In the early 21st century, baobabs in southern Africa began to die off
Adansonia
Family of instruction set architectures
{\displaystyle {\begin{matrix}{\mathtt {CS}}:\\{\mathtt {DS}}:\\{\mathtt {SS}}:\\{\mathtt {ES}}:\end{matrix}}\ \ {\begin{matrix}\\{\begin{bmatrix}{\mathtt
X86
Mathematical object
= B q ∗ / d {\displaystyle q=Bq^{\ast }/d} else return false where the matrix M is M = ( 0 ⋅ ⋅ ⋅ 0 ⋅ ⋅ I n − 1 ⋅ 0 ) {\displaystyle M={\begin{pmatrix}0&\cdot
Ideal_lattice
Group of unitary complex matrices with determinant of 1
A generic SU(3) group element generated by a traceless 3 × 3 Hermitian matrix H, normalized as tr(H2) = 2, can be expressed as a second order matrix polynomial
Special_unitary_group
Genus of nodosaurid dinosaurs
material allowed for a rescoring of its characters in their phylogenetic matrix. Based on these updates, they recovered Patagopelta within the Parankylosauria
Patagopelta
Branch of mathematics that studies abstract algebraic structures
elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The algebraic objects amenable to such a description
Representation_theory
American voice actor
Generic Racial Dark Elf, Generic Racial Troll, Generic Racial Ogre, Generic Racial Human, Generic Racial Kerra, Generic Racial Barbarian, Generic Racial
Michael_Gough_(voice_actor)
Scheme in algebraic geometry
X ′ → Y ′ ↓ ↓ X → Y {\displaystyle {\begin{matrix}X'&\to &Y'\\\downarrow &&\downarrow \\X&\to &Y\end{matrix}}} with f : X ′ → X {\displaystyle f:X'\to
Normal cone (algebraic geometry)
Normal_cone_(algebraic_geometry)
German plastics company
polyimide aurum TPI. The company's organisational structure is based on a matrix system, which is segmented into different business areas reflecting its
Ensinger_(company)
2024 film directed by Jeff Fowler
in an homage to voice actor Reeves having two characters, Neo from The Matrix and John Wick, who said the line before—though they decided against it,
Sonic_the_Hedgehog_3_(film)
Type of composite material
Cemented carbides are metal matrix composites where carbide particles act as the aggregate and a metallic binder serves as the matrix (analogous to concrete
Cemented_carbide
Mathematical symbols (+ and −)
consideration. Many algebraic structures, such as vector spaces and matrix rings, have some operation which is called, or is equivalent to, addition.
Plus_and_minus_signs
Partition of space by hyperplanes
Vadim Schechtman and Alexander Varchenko introduced a matrix indexed by the regions. The matrix element for the region R i {\displaystyle R_{i}} and R
Arrangement_of_hyperplanes
American voice actor and radio personality (1930–2021)
of his career, he also landed roles in stage productions at The Actor's Ring and the Portland Civic Theater. It was during his broadcasting career that
Jack_Angel
Form of carbon
promotes its own brands, or licensed product lines, rather than completely "generic" diamond products. The campaign was perhaps best captured by the slogan
Diamond
Scheme theory concept
is a morphism such that the induced map on every stalk is a flat map of rings, i.e., f P : O Y , f ( P ) → O X , P {\displaystyle f_{P}\colon {\mathcal
Flat_morphism
Taxon that disappears from the fossil record, only to reappear later
example, a trilobite that gets eroded out of its Cambrian-aged limestone matrix, and reworked into Miocene-aged siltstone. A ghost lineage is a pronounced
Lazarus_taxon
Kind of complex manifold
E\in {\text{Alt}}^{2}(\Lambda ,\mathbb {Z} )} by looking at a generic alternating matrix and finding the correct compatibility conditions for it to behave
Complex_torus
Genus of thyreophoran dinosaurs
several vertebrae, partial limb bones, and at least 120 osteoderms. The generic name, Yuxisaurus, combines a reference to the type locality in Yuxi, Yunnan
Yuxisaurus
1974–76 American children's television series
obelisk-shaped booths that were larger on the inside than the outside and housed matrix tables—stone tables studded with a grid of colored crystals. Uncontrolled
Land of the Lost (1974 TV series)
Land_of_the_Lost_(1974_TV_series)
Protestant Reformation ad fundum to the bottom i.e., "bottoms up!" (during a generic toast) or "back to the basics", depending on context. ad hoc to this i
List_of_Latin_phrases_(full)
2003 animated Disney film by Aaron Blaise and Robert Walker
grossing $18.6 million against new competing films such as Elf and The Matrix Revolutions, collecting $44.1 million in three weeks. The film grossed $85
Brother_Bear
Group representation
representation may be identified with the ordinary matrix transpose. Since the adjoint of a matrix is the complex conjugate of the transpose, the transpose
Dual_representation
Nonsteroidal anti-inflammatory drug
Aspirin (/ˈæsp(ə)rɪn/) is the genericized trademark for acetylsalicylic acid (ASA), a nonsteroidal anti-inflammatory drug (NSAID) used to reduce pain
Aspirin
American media franchise
most likely not make its 2021 release date due to his commitment to The Matrix Resurrections. He also revealed, during the same interview, that a 100-page
John_Wick
1997 film by Robert Zemeckis
Ellie's father, they planned to use an effect similar to bullet time from The Matrix to show him stopped in time as he died. As the movie was filmed, they found
Contact_(1997_American_film)
theory Crouzeix's conjecture: the matrix norm of a complex function f {\displaystyle f} applied to a complex matrix A {\displaystyle A} is at most twice
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Set of rules defining correctly structured programs
otherwise it is an inner product. An inner product intended for conventional matrix multiplication uses the + and × functions, replacing these with other dyadic
APL_syntax_and_symbols
Nitrogen-based molecule
stereochemistry. Arylnitrene ring-expansion and ring-contraction: Aryl nitrenes show ring expansion to 7-membered ring cumulenes, ring opening reactions and
Nitrene
Ankylosaurid dinosaur genus from the Late Cretaceous Period
Barnum Brown in 1908; it is monotypic, containing only A. magniventris. The generic name means "fused" or "bent lizard", and the specific name means "great
Ankylosaurus
Stories. Troll Books. ISBN 0-8167-0798-7. {{cite book}}: |first1= has generic name (help) Lewis, Elizabeth Foreman (11 May 1999). Young Fu of the Upper
List of group-0 ISBN publisher codes
List_of_group-0_ISBN_publisher_codes
France/Rising Star deal". GamesIndustry.biz. {{cite web}}: |last= has generic name (help) "Non-Sony Ghostbusters dated". July 27, 2009. "Easy Piano for
List of Bandai Namco video games
List_of_Bandai_Namco_video_games
in a matrix. The keyboard controller, often an 8-bit processor, parses columns one-by-one and recovers the state of 8 keys at once. This matrix scan process
Computer security compromised by hardware failure
Computer_security_compromised_by_hardware_failure
input the focal length and maximum aperture, therefore obtaining access to Matrix metering and display of the selected aperture: mass-market models still
Dandelion_chip
Group of fictional characters
as a knight who was captured by Hordak and thrown into the experimental matrix which grafted cybernetic parts to him. Fisto is an extra-strong warrior
List of He-Man and the Masters of the Universe characters
List_of_He-Man_and_the_Masters_of_the_Universe_characters
Gemstone: beryllium aluminium silicate
of beryl that can be found. Increasing alkali content within the silicate ring channels causes increases to the refractive indices and birefringence. Beryl
Beryl
game consoles. Early examples representing this shift include Enter the Matrix (2003) and The Chronicles of Riddick: Escape from Butcher Bay (2004). Custer's
List of video games notable for negative reception
List_of_video_games_notable_for_negative_reception
Type of mythogical creature in Irish mythology
Dullahan or Dulachan (Irish: Dubhlachan [Duḃlaċan]) referring to "hobgoblin" (generic term; cf. Dullahan described as "unseelie (wicked) fairy"), literally "signifies
Dullahan
Construct in algebraic geometry
definition to the general situation of a morphism of ringed topoi, thereby incorporating morphisms of ringed spaces, schemes, and algebraic spaces into the
Cotangent_complex
Concept in continental philosophy
the sensible realm; it "gives space" and has maternal overtones (a womb, matrix): “Moreover, a third kind is that of the Khôra (χώρας), everlasting, not
Khôra
Gamma-aminobutyric acid analog
approved for use in the United Kingdom in 1993. It has been available as a generic medication in the United States since 2004. It is the first of several
Gabapentin
Powder used to add or alter colour
masterbatch production, pigments are extruded or kneaded into a binder matrix at elevated processing temperatures. Upon cooling, the solid masterbatches
Pigment
C++ framework for compiler development
and performs the sum between the values at the same positions: func.func @matrix_add(%arg0: memref<10x20xf32>, %arg1: memref<10x20xf32>) -> memref<10x20xf32>
MLIR_(software)
Genus of lichens
type species. Closely related genera are Savoronala and Sprucidea. The generic name honours the Russian lichenologist Mikhail Zhurbenko, "for his magnificent
Zhurbenkoa
2013 video game
represent the mood matrix. As they wanted other characters to be able to see the mood matrix, it was decided to make Widget project the mood matrix as a hologram
Phoenix Wright: Ace Attorney – Dual Destinies
Phoenix_Wright:_Ace_Attorney_–_Dual_Destinies
French sociologist and philosopher (1929–2007)
Yorker. {{cite magazine}}: |first= has generic name (help) Genosko, Gary; Bryx, Adam, eds. (July 2004). "The Matrix Decoded: Le Nouvel Observateur Interview
Jean_Baudrillard
Aniconic representation of the Hindu goddess Shakti, consort of Shiva
such as the Nisvasa tattva samhita and Mohacudottara, the term pitha generically refers to the base and the yoni. The reverence for yoni, state Jones
Yoni
Fictional adoptive parents of Superman
Clark's adult life. In this version of events, after a Kryptonian "birthing matrix" lands on Earth, Jonathan and Martha find a newborn infant inside. Taking
Jonathan_and_Martha_Kent
GENERIC MATRIX-RING
GENERIC MATRIX-RING
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Female
English
French form of Latin Maria, MARIE means "obstinacy, rebelliousness" or "their rebellion."
Female
German
Pet form of German Katarine, KATRIN means "pure."
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
Male
English
Anglicized form of Irish Gaelic MainchÃn, MANNIX means "little monk."
Male
French
French and German form of Greek Mattathias, MATHIS means "gift of God."
Male
English
Middle English form of Anglo-Saxon Ceneric, CENRIC means "keen power."
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Female
Welsh
Medieval Welsh name, probably GENERYS means "white lady."Â
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
Italian
Italian form of Hebrew Mattithyah, MATTIA means "gift of God."
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Male
Swedish
Swedish variant spelling of Scandinavian Henrik, HENRIC means "home-ruler."
Male
German
Old German name, GOMERIC means "man-power."
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Male
German
Altered form of German Almeric, EMERIC means "work-power."
GENERIC MATRIX-RING
GENERIC MATRIX-RING
Girl/Female
Australian, Chinese, German, Greek, Spanish
Of the Nobility
Boy/Male
Tamil
Bhupendra | பூபேநà¯à®¤à¯à®°
King of the earth
Boy/Male
Muslim
Noble, Respected
Surname or Lastname
English
English : variant of Backus.
Boy/Male
Muslim
Kind hearted, Spiritual
Girl/Female
Australian, Spanish
Star
Male
African
God with us.
Boy/Male
Greek
One of Odysseus's men.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
A Line of Poem; Sentence; Pharse; Line of Words
Male
Greek
(Γάννης) Contracted form of Greek Yiannis, YANNIS means "God is gracious."Â
GENERIC MATRIX-RING
GENERIC MATRIX-RING
GENERIC MATRIX-RING
GENERIC MATRIX-RING
GENERIC MATRIX-RING
n.
The cavity in which anything is formed, and which gives it shape; a die; a mold, as for the face of a type.
n.
The earthy or stony substance in which metallic ores or crystallized minerals are found; the gangue.
a.
Of or pertaining to the Maoris or to their language.
a.
Usual; common, on most occasions; as, his general habit or method.
a.
Alt. of Generical
n.
A rectangular arrangement of symbols in rows and columns. The symbols may express quantities or operations.
a.
Pertaining to a genus or kind; relating to a genus, as distinct from a species, or from another genus; as, a generic description; a generic difference; a generic name.
pl.
of Postmaster-general
n.
A mold; a matrix.
pl.
of Matrix
n.
Hence, that which gives form or origin to anything
n.
See Matrix.
n.
Alt. of Gentrie
n.
The lifeless portion of tissue, either animal or vegetable, situated between the cells; the intercellular substance.
a.
Of or pertaining to the meter as a standard of measurement; of or pertaining to the decimal system of measurement of which a meter is the unit; as, the metric system; a metric measurement.
n.
A housekeeper; esp., a woman who manages the domestic economy of a public instution; a head nurse in a hospital; as, the matron of a school or hospital.
a.
Common to many, or the greatest number; widely spread; prevalent; extensive, though not universal; as, a general opinion; a general custom.
n.
The five simple colors, black, white, blue, red, and yellow, of which all the rest are composed.
pl.
of Maori