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group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of...

mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

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...

In linear algebra, an invertible matrix is a square matrix which has an inverse. In other words, if some other matrix is multiplied by the invertible matrix...

As the computation of the kernel of a matrix is a special instance of solving a homogeneous system of linear equations, the kernel may be computed with...

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 linear...

{\displaystyle K^{m}} are given. Any m × n {\displaystyle m\times n} matrix A induces a linear operator from K n {\displaystyle K^{n}} to K m {\displaystyle...

In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗ U = U...

{\displaystyle 2\times 3} matrix", or a matrix of dimension 2 × 3 {\displaystyle 2\times 3} . Matrices are commonly related to linear algebra. Notable exceptions...

generally non-linear transformation matrices. With respect to an n-dimensional matrix, an n+1-dimensional matrix can be described as an augmented matrix. In 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 linear algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has...

multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linear algebra libraries; the...

mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices....

In mathematics, and in particular linear algebra, the Moore–Penrose inverse ⁠ A + {\displaystyle A^{+}} ⁠ of a matrix ⁠ A {\displaystyle A} ⁠, often called...

whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as...

of a linear space with a basis. Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group...