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The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^(-1) such that AA^(-1)=I, (1) where I is the identity matrix. Courant and Hilbert (1989, ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

Given an m×n matrix B, the Moore-Penrose generalized matrix inverse is a unique n×m matrix pseudoinverse B^+. This matrix was independently defined by Moore in 1920 and ...

The notion of an inverse is used for many types of mathematical constructions. For example, if f:T->S is a function restricted to a domain S and range T in which it is ...

The Drazin inverse is a matrix inverse-like object derived from a given square matrix. In particular, let the index k of a square matrix be defined as the smallest ...

A square matrix A such that A^2=I, where I is the identity matrix. An involutory matrix is its own matrix inverse.

The power A^n of a matrix A for n a nonnegative integer is defined as the matrix product of n copies of A, A^n=A...A_()_(n). A matrix to the zeroth power is defined to be the ...

The process of computing a matrix inverse.

An n×m matrix A^- is a 1-inverse of an m×n matrix A for which AA^-A=A. (1) The Moore-Penrose matrix inverse is a particular type of 1-inverse. A matrix equation Ax=b (2) has ...

A square matrix which is not reducible is said to be irreducible.