281 citations · 2.1k across the 125 of their papers we have counts for
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The minimization of matrix logarithms - on a fundamental property of the unitary polar factor
Johannes Lankeit, Patrizio Neff, Yuji Nakatsukasa
We show that the unitary factor U in the polar decomposition of a nonsingular matrix Z = U H is the minimizer for both ||Log(Q^* Z)|| and ||sym (Log(Q^*Z))|| over unitary Q, for an…
A Riemannian approach to strain measures in nonlinear elasticity
Patrizio Neff, Bernhard Eidel, Frank Osterbrink +1
The isotropic Hencky strain energy appears naturally as a distance measure of the deformation gradient to the set SO(n) of rigid rotations in the canonical left-invariant Riemannia…
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 in the polar decomposition of the matrix is the minimizer for both and its Hermitian part $\| \mathrm{sym Log}(Q^…
Sum of squared logarithms - An inequality relating positive definite matrices and their matrix logarithm
Mircea Birsan, Patrizio Neff, Johannes Lankeit
Let y1, y2, y3, a1, a2, a3 > 0 be such that y1 y2 y3 = a1 a2 a3 and y1 + y2 + y3 >= a1 + a2 + a3, y1 y2 + y2 y3 + y1 y3 >= a1 a2 + a2 a3 + a1 a3. Then the following inequality hold…