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Hermitian-type generalized singular value decomposition with applications

Authors


Yonghui Liu, Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, China.

E-mail: liuyh@shfc.edu.cn

SUMMARY

For a pair of given Hermitian matrix A and rectangular matrix B with the same row number, we reformulate a well-known simultaneous Hermitian-type generalized singular value decomposition (HGSVD) with more precise structure and parameters and use it to derive some algebraic properties of the linear Hermitian matrix function ABXB* and Hermitian solution of the matrix equation BXB* = A, and the canonical form of a partitioned Hermitian matrix and some optimization problems on its inertia and rank. Copyright © 2012 John Wiley & Sons, Ltd.

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