Basic Examples (1) 

Compute the polar decomposition for a 4×3 matrix:

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Scope (2) 

Compute the polar decomposition of a complex matrix:

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A matrix with entries having 20-digit precision:

The polar decomposition is computed using the full 20-digit precision of the input:

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Properties and Relations (2) 

A random 5×4 matrix m:

Compute its polar decomposition:

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The columns of q are orthonormal:

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The matrix s is Hermitian positive semidefinite:

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The matrix s is equal to MatrixPower[ConjugateTranspose[m].m,1/2]:

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m is equal to q.s:

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If the matrix m is Hermitian positive semidefinite, then q is equal to the identity matrix, and s is equal to m:

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Possible Issues (1) 

PolarDecomposition only works with approximate numerical matrices:

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