first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB. Matrix multiplication was first described by the French...

Matrix AB is a 2015 Czech documentary film by Vít Klusák. It centers on Czech politician and businessman Andrej Babiš whom Klusák filmed for about one...

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element...

multiplication. Matrix norms are particularly useful if they are also sub-multiplicative:   ‖ A B ‖ ≤ ‖ A ‖ ‖ B ‖   {\displaystyle \ \left\|AB\right\|\leq...

defined for a square matrix (n × n). The trace of a matrix is the sum of its eigenvalues (counted with multiplicities). Also, tr(AB) = tr(BA) for any matrices...

of the right matrix. If A is an m×n matrix and B is an n×p matrix, then their matrix product AB is the m×p matrix whose entries are given by the dot product...

classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though that...

runtime complexity. If A is a 10 × 30 matrix, B is a 30 × 5 matrix, and C is a 5 × 60 matrix, then computing (AB)C needs (10×30×5) + (10×5×60) = 1500 +...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number...

A^{+}} ⁠ of a matrix ⁠ A {\displaystyle A} ⁠, often called the pseudoinverse, is the most widely known generalization of the inverse matrix. It was independently...

n-by-n square matrix A is called invertible if there exists an n-by-n square matrix B such that A B = B A = I n , {\displaystyle \mathbf {AB} =\mathbf {BA}...

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...

( A B = B A {\displaystyle AB=BA} ) if they are simultaneously diagonalizable (that is, there exists an invertible matrix P {\displaystyle P} such that...

transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing...

mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n {\displaystyle...

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...

Proposition—If A and B are normal with AB = BA, then both AB and A + B are also normal. Furthermore there exists a unitary matrix U such that UAU* and UBU* are...

blockwise matrix inversion. While the identity is primarily used on matrices, it holds in a general ring or in an Ab-category. The Woodbury matrix identity...

algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It...

The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries c i j =...

Institute for Politics and Society Senate Caucus Young ANO History and related topics 2017 Czech government crisis 2018 Czech political crisis Matrix AB...

{\displaystyle \det(AB)=\left|{\begin{matrix}1&1\\3&1\end{matrix}}\right|\cdot \left|{\begin{matrix}1&1\\3&1\end{matrix}}\right|+\left|{\begin{matrix...

rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an orthogonal matrix R T...

linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the...

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{...

In mathematics, a symmetric matrix M {\displaystyle M} with real entries is positive-definite if the real number x T M x {\displaystyle \mathbf {x} ^{\mathsf...

of matrix A, and there is a zero entry in the same position of the matrix product AB. In this construction, the nonzero elements of the matrix AB represent...

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...

superscript T denotes the matrix transpose, that is, tr ⁡ ( A B T ) = 1 T ( A ⊙ B ) 1 {\displaystyle \operatorname {tr} \left(AB^{\mathsf {T}}\right)=\mathbf...

In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns...