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Block diagonal matrix of Jordan blocks
the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities
Jordan_matrix
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known as "Jordan blocks". Each Jordan block contains
Jordan_normal_form
French mathematician (1838–1922)
of results: The Jordan curve theorem, a topological result required in complex analysis The Jordan normal form and the Jordan matrix in linear algebra
Camille_Jordan
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
Algorithm for solving systems of linear equations
Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss–Jordan elimination. In this case, the term Gaussian
Gaussian_elimination
American media franchise
The Matrix is an American cyberpunk media franchise consisting of four feature films, beginning with The Matrix (1999) and continuing with three sequels
The_Matrix_(franchise)
Matrix which differs from the identity matrix by one elementary row operation
elimination to reduce a matrix to row echelon form. They are also used in Gauss–Jordan elimination to further reduce the matrix to reduced row echelon
Elementary_matrix
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
2021 film by Lana Wachowski
The Matrix Resurrections is a 2021 American science fiction action film co-produced and directed by Lana Wachowski, who co-wrote the screenplay with David
The_Matrix_Resurrections
Soft carbonated drink
Matrix Carbonated Drink is a carbonated soft drink produced in Jordan by Defaf Al-Nahrayn Company, a Jordanian beverage and snacks company established
Matrix_Carbonated_Drink
Matrix operation which flips a matrix over its diagonal
that flips a matrix over its diagonal; that is, transposition switches the row and column indices of the matrix A to produce another matrix, called the
Transpose
Non-diagonalizable matrix; one lacking a basis of eigenvectors
n} . Any defective matrix has a nontrivial Jordan normal form, which is as close as one can come to diagonalization of such a matrix. A simple example
Defective_matrix
Equivalence under a change of basis (linear algebra)
can be immediately read off from a matrix in Jordan form, but they can also be determined directly for any matrix by computing the Smith normal form,
Matrix_similarity
2003 film by the Wachowskis
Matrix Revolutions is a 2003 American science fiction action film written and directed by the Wachowskis. It is the third installment in The Matrix film
The_Matrix_Revolutions
Matrices similar to diagonal matrices
defective matrix can be deformed into a diagonalizable matrix by a small perturbation; and the Jordan–Chevalley decomposition states that any matrix is uniquely
Diagonalizable_matrix
Topics referred to by the same term
mathematics, Jordan decomposition may refer to Hahn decomposition theorem, and the Jordan decomposition of a measure Jordan normal form of a matrix Jordan–Chevalley
Jordan_decomposition
Representation of a matrix as a product
algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;
Matrix_decomposition
Vector satisfying some of the criteria of an eigenvector
"almost diagonal matrix" J {\displaystyle J} in Jordan normal form, similar to A {\displaystyle A} , which is useful in computing certain matrix functions of
Generalized_eigenvector
A matrix canonical form
linear algebra, a Weyr canonical form (or, Weyr form or Weyr matrix) is a square matrix which (in some sense) induces "nice" properties with matrices
Weyr_canonical_form
Special kind of square matrix
In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal
Triangular_matrix
Matrix equal to its conjugate-transpose
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose
Hermitian_matrix
Matrix equal to its transpose
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A is symmetric ⟺ A = A T . {\displaystyle A{\text{
Symmetric_matrix
Formulation of quantum mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually
Matrix_mechanics
Possible form of a matrix
elimination that transforms a matrix to reduced row echelon form is sometimes called Gauss–Jordan elimination. A matrix is in column echelon form if its
Row_echelon_form
Matrix operation generalizing exponentiation of scalar numbers
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems
Matrix_exponential
Matrix decomposition
(also known as eigenvalue decomposition or EVD) is a factorization of a matrix A {\displaystyle A} into a canonical form given by A = Q D Q − 1 {\displaystyle
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Matrix whose only nonzero elements are on its main diagonal
diagonal entries of a matrix. Anti-diagonal matrix Banded matrix Bidiagonal matrix Diagonally dominant matrix Diagonalizable matrix Jordan normal form Multiplication
Diagonal_matrix
Mathematical operation on invertible matrices
mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization
Logarithm_of_a_matrix
Function that maps matrices to matrices
notion is the Jordan–Chevalley decomposition which expresses a matrix as a sum of a diagonalizable and a nilpotent part. A Hermitian matrix has all real
Analytic_function_of_a_matrix
real matrix and to a Hermitian matrix. There is a standard form for the consimilarity class, analogous to the Jordan normal form. Hong, YooPyo; Horn
Matrix_consimilarity
Square matrix constructed from a monic polynomial
In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots
Companion_matrix
Matrix with non-zero elements only in a diagonal band
In mathematics, particularly matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising
Band_matrix
Russian mathematician, computer scientist and entrepreneur (born 1962)
Calligraph hyphenation system, the Sphinx full-text search engine, and the Jordan matrix calculator. During the 1991 Soviet coup d'état attempt, most of ORFO
Igor_Ashmanov
Polynomial whose roots are the eigenvalues of a matrix
algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It
Characteristic_polynomial
Matrix of inner products of vectors
Gram matrix (or Gramian matrix, Gramian) of vectors v 1 , … , v n {\displaystyle v_{1},\dots ,v_{n}} in an inner product space is the Hermitian matrix of
Gram_matrix
Matrix defined using smaller matrices called blocks
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices
Block_matrix
In matrix theory, the Frobenius covariants of a square matrix A are special polynomials of it, namely projection matrices Fi(A) associated with the eigenvalues
Frobenius_covariant
Sum of elements on the main diagonal
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle
Trace_(linear_algebra)
Mathematical expression for linear operators
x} . Indeed, it suffices to check this for the decomposition of the Jordan matrix J = D + R {\displaystyle J=D+R} . This is a technical argument, but
Jordan–Chevalley decomposition
Jordan–Chevalley_decomposition
Canadian actress (born 1967)
television, she rose to international prominence for her role of Trinity in The Matrix series (1999–present). She has starred in Memento (2000), for which she
Carrie-Anne_Moss
Matrix B such that B² equals a given matrix A
square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is
Square_root_of_a_matrix
Mathematical concept in algebra
In linear algebra, a nilpotent matrix is a square matrix N such that N k = 0 {\displaystyle N^{k}=0\,} for some positive integer k {\displaystyle k}
Nilpotent_matrix
Kind of square matrix in linear algebra
algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has zero entries
Hessenberg_matrix
since it does not require inverting a matrix. This example illustrates a generalized modal matrix with four Jordan chains. Unfortunately, it is a little
Modal_matrix
2021 film by Denzel Washington
Office, Is There Room For 'Matrix', 'Sing 2' & 'King's Man'?". Deadline Hollywood. Retrieved December 21, 2021. "A Journal for Jordan (2021)". Box Office Mojo
A_Journal_for_Jordan
This is a list of awards and nominations received by The Matrix franchise. The Matrix is a 1999 science fiction action film. It spawned three sequels,
List of accolades received by The Matrix film series
List_of_accolades_received_by_The_Matrix_film_series
Concepts from linear algebra
the diagonal matrix of eigenvalues generalizes to the Jordan normal form. Over an algebraically closed field, any matrix A has a Jordan normal form and
Eigenvalues_and_eigenvectors
German physicist and politician (1902–1980)
the mathematical form of matrix mechanics, and developed canonical anticommutation relations for fermions. He introduced Jordan algebras in an effort to
Pascual_Jordan
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries
List_of_named_matrices
Governing body of association football in Jordan
Royal Jordanian Official mansaf partner: Kasih Official insurance: Jordan Insurance Company Official clothing partner: Kelme Official drink: Matrix Official
Jordan_Football_Association
Canonical form of matrices over a field
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 obtained by
Frobenius_normal_form
Matrices named after Élie Cartan
In mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan. Amusingly, the Cartan matrices
Cartan_matrix
Polynomial with a matrix as variable
of an eigenvalue is the size of its largest Jordan block). Matrix polynomials can be used to sum a matrix geometrical series as one would an ordinary
Matrix_polynomial
Matrix (1999). The film was a commercial success and received critical acclaim. He reprised the role in its sequels, The Matrix Reloaded, The Matrix Revolutions
Keanu_Reeves_filmography
Matrix decomposition
complex matrix into a rotation, followed by a scaling, followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with
Singular_value_decomposition
Math operation methods
In linear algebra, the inverse square matrix A {\displaystyle A} is another square matrix A − 1 {\displaystyle A^{-1}} such that the product A − 1 A {\displaystyle
Methods_of_matrix_inversion
Algebraic structure with addition and multiplication
Jordan matrix. Thus, if, say, k is algebraically closed, then all pi's are of the form t – λi and the above decomposition corresponds to the Jordan canonical
Ring_(mathematics)
Theorem in linear algebra
In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron (1907) and extended by Georg Frobenius (1912), asserts that a
Perron–Frobenius_theorem
Japanese television series
Chilean, Malian, Jordanian, and Dutch watching and voting each shows, Including an English narrator who speaks the shows title in English. Matrix Ping Pong is
Kasou_Taishou
Drazin inverse is invariant under matrix conjugations, writing A = P J P − 1 {\displaystyle A=PJP^{-1}} , where J is in Jordan normal form, implies that A D
Drazin_inverse
elimination Gauss–Jordan elimination Overcompleteness Strassen algorithm Matrix Matrix addition Matrix multiplication Basis transformation matrix Characteristic
Outline_of_linear_algebra
Vectors mapped to 0 by a linear map
in matrix form as: [ 2 3 5 0 − 4 2 3 0 ] . {\displaystyle \left[{\begin{array}{ccc|c}2&3&5&0\\-4&2&3&0\end{array}}\right].} Through Gauss–Jordan elimination
Kernel_(linear_algebra)
American actor (born 1967)
(1991–1993), real-life activist Huey P. Newton in Panther (1995), and Tank in The Matrix (1999). Chong was born in Seattle on July 8, 1967, to an African-American
Marcus_Chong
Standard representation of a mathematical object
example: Jordan normal form is a canonical form for matrix similarity. The row echelon form is a canonical form, when one considers as equivalent a matrix and
Canonical_form
Mathematical concept in algebra
Matrices A {\displaystyle A} that commute with matrix B {\displaystyle B} are called the commutant of matrix B {\displaystyle B} (and vice versa). A set
Commuting_matrices
American actor (born 1986)
drama The Trial of the Chicago 7 (2020), and Morpheus / Agent Smith in The Matrix Resurrections (2021). For his portrayal of Cal Abar / Doctor Manhattan in
Yahya_Abdul-Mateen_II
Algorithms for matrix decomposition
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra
Non-negative matrix factorization
Non-negative_matrix_factorization
Tool in linear algebra and matrix analysis
is a (p + q) × (p + q) matrix. If D is invertible, then the Schur complement of the block D of the matrix M is the p × p matrix defined by M / D := A −
Schur_complement
Topics referred to by the same term
classical adjoint) of a matrix in mathematics Adjukru language, ISO-639-3 code Amman Civil Airport in Amman Governorate, Jordan (IATA airport code ADJ)
ADJ
Generalization of signum function to matrices
In mathematics, the matrix sign function is a matrix function on square matrices analogous to the complex sign function. It was introduced by J.D. Roberts
Matrix_sign_function
American actor (born 1963)
to appear as Mercutio in Romeo+Juliet (1996) and Link in The Matrix Reloaded and The Matrix Revolutions (both 2003). On television, he has starred as Augustus
Harold_Perrineau
Square matrices satisfy their characteristic equation
mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers)
Cayley–Hamilton_theorem
American stuntman and film director
and coordinator, notably as the key stunt double for Keanu Reeves on The Matrix (1999), and as the martial arts stunt coordinator on its first two sequels
Chad_Stahelski
American computer scientist and statistician
advised by Michael I. Jordan, included work on sparse principal components analysis (PCA) for gene expression modeling, low-rank matrix completion for recommender
Lester_Mackey
Space within the inner membrane of the mitochondrion
mitochondrion, the matrix is the space within the inner membrane. It can also be referred as the mitochondrial fluid. The word "matrix" stems from the fact
Mitochondrial_matrix
Method of data analysis
the data's covariance matrix. Thus, the principal components are often computed by eigendecomposition of the data covariance matrix or singular value decomposition
Principal_component_analysis
Stochastic matrix representing links between entities
A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links
Google_matrix
Hard keratin protection of digit
plate, the nail matrix and the nail bed below it, and the grooves surrounding it. The nail matrix is the active tissue (or germinal matrix) that generates
Nail_(anatomy)
DC Comics superheroine
taken up the mantle of Supergirl, sometimes at the same time, including Matrix, Linda Danvers and Cir-El. Created as a female counterpart to Superman,
Supergirl
Linear operator
also known as Jacobi matrix, is a symmetric linear operator acting on sequences which is given by an infinite tridiagonal matrix. It is commonly used
Jacobi_operator
Study of matrices and their algebraic properties
(such as matrix addition, matrix multiplication and operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm
Matrix_analysis
Type of mathematical equation
that the matrix A be diagonalizable and bypasses complexities of the Jordan canonical forms normally utilized. A first-order homogeneous matrix ordinary
Matrix_differential_equation
US visual effects company
for their groundbreaking visual effects on the 1999 sci-fi classic The Matrix, most notably creating the iconic "Bullet Time" sequence. Though a small
Manex_Visual_Effects
Branch of mathematics
and makes the characteristic polynomial immediately readable on the matrix. The Jordan normal form requires to extension of the field of scalar for containing
Linear_algebra
Vector spaces associated to a matrix
image) of a matrix A {\displaystyle A} is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the
Row_and_column_spaces
Basis of a type of algebraic structure
independent generalized eigenvectors of an n×n matrix A {\displaystyle A} , if the set is composed entirely of Jordan chains. In representation theory, it refers
Canonical_basis
Algebraic term
matrix M is a unipotent matrix if and only if its characteristic polynomial P(t) is a power of t − 1. Thus all the eigenvalues of a unipotent matrix are
Unipotent
American award for achievements in media
The Matrix Awards is an awards ceremony held annually by the New York Women in Communications, Inc. The award was created in the 1930s by Theta Sigma Phi
Matrix_Awards
Relates theta constants to the branch points of a hyperelliptic curve
\left({\begin{matrix}1/2&0&\cdots &0\\0&\cdots &0&0\end{matrix}}\right)(\Omega )\right]^{4}\left[\theta \left({\begin{matrix}1/2&1/2&0&\cdots &0\\0&\cdots
Thomae's_formula
American actor (born 1974)
began his career as a regular on television series Crossing Jordan (2001–2002) and Threat Matrix (2003–2004), before his breakthrough role as Richard Tyler
Mahershala_Ali
Recursive algorithm for matrix multiplication
named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix multiplication algorithm for large matrices,
Strassen_algorithm
German–British physicist (1882–1970)
picture as they did in the matrix formulation of quantum mechanics. With the help of his assistant and former student Pascual Jordan, he began immediately
Max_Born
American politician (born 1935)
controversial program called Matrix which aimed to deal with the city's homelessness problems. During his mayoral tenure Jordan played a role in converting
Frank_Jordan
German physicist (1901–1976)
subsequent series of papers with Max Born and Pascual Jordan, during the same year, his matrix formulation of quantum mechanics was substantially elaborated
Werner_Heisenberg
Result about when a matrix can be diagonalized
result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful
Spectral_theorem
Development in Amman, Jordan
New Abdali is an area in the Al-Abdali district in Amman, Jordan. Its development plan, launched in 2005, consisting of hotels, apartments, offices, commercial
New_Abdali
In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of
Albert_algebra
Largest absolute value of an operator's eigenvalues
In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of
Spectral_radius
Theorem in matrix analysis
Crouzeix's conjecture is a problem in matrix analysis proposed by Michel Crouzeix in 2004, and it can be stated as follows: ‖ f ( A ) ‖ ≤ 2 sup z ∈ W (
Crouzeix's_conjecture
Burmese-American mixed martial artist
of the Year". Sherdog. Retrieved December 23, 2025. "MMA Awards". Fight Matrix. Retrieved January 2, 2026. Hannoun, Farah. "MMA Junkie's 2025 Breakout
Joshua_Van
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JORDAN MATRIX
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