MathAlgebraLinear algebraMatrix decomposition

Pseudoinverse

A versatile tool

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Take a system of equations $A \mathbf{x} = \mathbf{b}$ .

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^{\dag}

reduces to

A^{-1}

A^{\dag}

computes the projection of

\mathbf{b}

A^{\dag}

finds the smallest solution

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