A note on the factorization of some structured matrix functions
Ilya M. Spitkovsky, Anatoly F. Voronin
TL;DR
This paper investigates conditions under which certain structured block matrix functions can be factorized, focusing on cases where the diagonal block is positive definite and off-diagonal blocks are conjugates, using the Schur complement.
Contribution
It provides new criteria for factorization of structured matrix functions based on the Schur complement, especially for matrices with specific symmetry and positivity properties.
Findings
Conditions for factorability with zero partial indices
Factorization criteria involving the Schur complement
Application to matrices with conjugate off-diagonal blocks
Abstract
Let G be a block matrix function with one diagonal block A being positive definite and the off diagonal blocks complex conjugates of each other. Conditions are obtained for G to be factorable (in particular, with zero partial indices) in terms of the Schur complement of A.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.