Definition:Inverse Matrix/Left
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This page is about Left Inverse Matrix. For other uses, see Left Inverse.
Definition
Let $m, n \in \Z_{>0}$ be a (strictly) positive integer.
Let $\mathbf A = \sqbrk a_{m n}$ be a matrix of order $m \times n$.
Let $\mathbf B = \sqbrk b_{n m}$ be a matrix of order $n \times m$ such that:
- $\mathbf B \mathbf A = \mathbf I_n$
where $\mathbf I_n$ denotes the unit matrix of order $n$.
Then $\mathbf B$ is known as a left inverse (matrix) of $\mathbf A$.
Also see
Sources
- 1998: Richard Kaye and Robert Wilson: Linear Algebra ... (previous) ... (next): Part $\text I$: Matrices and vector spaces: $1$ Matrices: $1.3$ The inverse of a matrix