MathAlgebraLinear algebraMatrix decomposition

Positive definite matrices

The pieces of the polar decomposition

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Take a square matrix $M$ and consider its polar decomposition:

$M = U\ |M|$ When $M$ is invertible, you can explicitly get matrix $U$ in terms of $M$ and $| M |$ .

To do this, multiply both sides of the equation by the inverse of $U$ , and then solve for $U$ on the left side of the resulting equation.

Select one option from the list

U= (M^{-1} |M|) ^T

U= M^{-1} |M|

U= |M| \ M^{-1}

U= (|M| \ M^{-1}) ^T

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