Definition:Pseudoinverse of Linear Transformation

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Definition

Let $U, V$ be vector spaces.

Let $S: U \to V$ be a linear transformation.

Let $T: V \to U$ be a linear transformation.


$S$ and $T$ are pseudoinverse to each other if and only if:

$T \circ S - I_U$ is degenerate

and:

$S \circ T - I_V$ is degenerate

where:

$\circ$ denotes the composition
$I_U$ denotes the identity mapping of $U$
$I_V$ denotes the identity mapping of $V$



Also see


Sources