MathAlgebraLinear algebraMatrix decomposition

Pseudoinverse

Theory

A versatile tool

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Take a system of equations Ax=bA \mathbf{x} = \mathbf{b}.

Assign the application of the pseudoinverse to each possible case.

Match the items from left and right columns
There is a unique solution
There are infinite possible solutions
There are no solutions
A†A^{\dag} reduces to A−1A^{-1}
A†A^{\dag} computes the projection of b\mathbf{b}
A†A^{\dag} finds the smallest solution

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