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...

the left matrix is the same as the number of rows 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...

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

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...

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...

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...

of Pauli matrices. The trace of a matrix is the sum of its eigenvalues (counted with multiplicities). Also, tr(AB) = tr(BA) for any matrices A and B...

{\displaystyle \mathbf {AB} =\mathbf {BA} =\mathbf {I} _{n},} where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication...

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 +...

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

tr(AB). The matrix ring Mn(R) can be identified with the ring of endomorphisms of the free right R-module of rank n; that is, Mn(R) ≅ EndR(Rn). Matrix multiplication...

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

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...

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...

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{...

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

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...

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...

the matrix product AB to be defined. In this case, we say that A and B are conformable for multiplication (in that sequence). Since squaring a matrix involves...

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...

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...

{\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...

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...

{\displaystyle |\Psi _{AB}\rangle =|\phi _{A}\rangle |\phi _{B}\rangle } is a separable state, then the reduced density matrix ρ A = Tr B ⁡ | Ψ A B ⟩...

In mathematics, a symplectic matrix is a 2 n × 2 n {\displaystyle 2n\times 2n} matrix M {\displaystyle M} with real entries that satisfies the condition...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

matrices which commute with each other (i.e. AB = BA) then AB is also involutory. If A is an involutory matrix then every integer power of A is involutory...

commutativity. An inverse of square matrix A is a matrix B (necessarily of the same dimension as A) such that AB = I. Equivalently, BA = I. An inverse...