A logarithmic minimization property of the unitary polar factor in the spectral norm and the Frobenius matrix norm

Patrizio Neff, Yuji Nakatsukasa, Andreas Fischle

The unitary polar factor $Q=U$ in the polar decomposition of the matrix $Z=UH$ is the minimizer for both $\Vert \mathrm{Log}(Q^{\ast }Z){\Vert }^2$ and its Hermitian part $\| \mathrm{sym Log}(Q^…