Left and Right Inverses of Matrices

Types: Not Applicable
Examples: Not Applicable
Constructions: Not Applicable
Generalizations: Not Applicable

Properties: Not Applicable
Sufficiencies: Not Applicable
Equivalences: Not Applicable
Justifications: Not Applicable

Left and Right Inverses of Matrices

Let be a Matrix. If there is a matrix such that , then is a left inverse of . If there is a matrix such that , then is a right inverse of .

Example: The matrix does not have a right or left inverse. To see this, assume it has a right inverse. Then there exists a matrix such that
But that product is , with 0 in the bottom right corner, not the required 1. A similar computation shows that there is no left inverse.