Orthogonality of matrices in the Ky Fan $k$-norms

Priyanka Grover

arXiv:1605.05649·math.FA·December 26, 2016

Orthogonality of matrices in the Ky Fan $k$-norms

Priyanka Grover

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TL;DR

This paper characterizes when matrices are orthogonal in Ky Fan k-norms, providing necessary and sufficient conditions for Birkhoff-James orthogonality in matrix spaces.

Contribution

It introduces new criteria for Birkhoff-James orthogonality of matrices in Ky Fan k-norms, extending understanding of matrix orthogonality.

Findings

01

Necessary and sufficient conditions for orthogonality in Ky Fan k-norms.

02

Characterization of orthogonality to subspaces of matrix space.

03

Extension of orthogonality concepts in matrix analysis.

Abstract

We obtain necessary and sufficient conditions for a matrix $A$ to be Birkhoff-James orthogonal to another matrix $B$ in the Ky Fan $k$ -norms. A characterization for $A$ to be Birkhoff-James orthogonal to any subspace $W$ of $M (n)$ is also obtained.

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