Matrix Inverse

Matrix Inverse

The inverse of a square matrix , sometimes called a reciprocal matrix, is a matrix such that (1) where is the identity matrix. Courant and Hilbert (1989, p. 10) use the notation to denote the inverse matrix. A square matrix has an inverse iff the determinant (Lipschutz 1991, p. 45). A matrix possessing an inverse is called nonsingular, or invertible. The matrix inverse of a square matrix may be taken in Mathematica using the function Inverse[m]. For a matrix (2) the matrix inverse is (3) (4) For a matrix (5) the matrix inverse is determinant of A is , (6) A general matrix can be inverted using methods such as the Gauss-Jordan elimination, Gaussian elimination, or LU decomposition. The inverse of a product of matrices and can be expressed in terms of and . Let (7) Then (8) and (9) Therefore, (10) so (11) where is the identity matrix, and (12) SEE ALSO: Gauss-Jordan Elimination, Gaussian Elimination, LU Decomposition, Matrix, Matrix 1-Inverse, Matrix Addition, Matrix Multiplication, Moore-Penrose Matrix Inverse, Nonsingular Matrix, Pseudoinverse, Singular Matrix, Strassen Formulas. [Pages Linking Here]