Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Inverse Matrix

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1153-7_200342

For a square m × m matrix A, the inverse matrix A−1 is also an m × m matrix such that A−1A = I = AA−1, where I is the identity matrix. If a matrix has an inverse, then its inverse is unique and the matrix is said to be nonsingular. If an inverse does not exist, the matrix is said to be singular. A nonsingular matrix has a nonzero value for its determinant; a singular matrix has a determinant value equal to zero.

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© Springer Science+Business Media New York 2013