invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their inverse. An n-by-n square matrix A is...

established. Since for invertible matrices the pseudoinverse equals the usual inverse, only examples of non-invertible matrices are considered below. For A...

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary...

own inverse, which implies that a reflection matrix is symmetric (equal to its transpose) as well as orthogonal. The product of two rotation matrices is...

In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows...

operations that are not defined for all possible operands, such as inverse matrices and inverse functions. This has been generalized to category theory, where...

generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized...

article lists some important classes of matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular...

orthogonal, with its inverse equal to its transpose: P − 1 = P T {\displaystyle P^{-1}=P^{\mathsf {T}}} .: 26  Indeed, permutation matrices can be characterized...

product: ch. 5  or Schur product) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding...

primarily used on matrices, it holds in a general ring or in an Ab-category. The Woodbury matrix identity allows cheap computation of inverses and solutions...

mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of...

The matrices of concepts are a conceptual tool put forth by philosopher Paul Franceschi, that aim at providing an alternative to the semiotic square described...

matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must...

the known points. This method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's I). The name given to...

order n {\displaystyle n} . Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear...

matrices. While there is no simple algorithm to directly calculate eigenvalues for general matrices, there are numerous special classes of matrices where...

A Bohemian matrix family is a set of matrices whose entries are members of a fixed, finite, and discrete set, referred to as the "population". The term...

than zero. The set of positive matrices is the interior of the set of all non-negative matrices. While such matrices are commonly found, the term "positive...

generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few classes...

matrices are M-matrices. An example is ( − 1 3 2 − 4 ) {\displaystyle \left({\begin{smallmatrix}-1&3\\2&-4\end{smallmatrix}}\right)} , whose inverse is...

"inverse" of the covering map. By properties of covering maps, the inverse can be chosen ono-to-one as a local section, but not globally. The matrices...

satisfactory. The inverse iteration algorithm requires solving a linear system or calculation of the inverse matrix. For non-structured matrices (not sparse...

square matrices (first minors) are required for calculating matrix cofactors, which are useful for computing both the determinant and inverse of square...

equal to its own inverse. In this group, two square matrices have the identity matrix as their product exactly when they are the inverses of each other....

represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal...

1 ( b ) , J f ( a ) {\displaystyle Jf^{-1}(b),Jf(a)} are the Jacobian matrices representing ( f − 1 ) ′ ( b ) , f ′ ( a ) {\displaystyle (f^{-1})'(b)...

gate "Hadamard Matrices and Designs" (PDF). UC Denver. Retrieved 11 February 2023. J.J. Sylvester. Thoughts on inverse orthogonal matrices, simultaneous...

lines, which break it up, or partition it, into a collection of smaller matrices. For example, the 3x4 matrix presented below is divided by horizontal and...

without reference to matrices (nor the components thereof) as the set of all linear maps X → X for which the adjoint equals the inverse. Over a complex vector...