Structured Canonical Forms For Products Of (Skew-) Symmetric Matrices And The Matrix Equation XAX = B

The contragredient transformation A bar right arrow P-1 AP-(inverted perpendicular) , B bar right arrow P-inverted perpendicular BP of two matrices A, B effects simultaneous similarity transformations of the products AB and BA. This work provides structured canonical forms under this transformation for symmetric or skew-symmetric A, B. As an application, these forms are used to study the quadratic matrix equation XAX = B, where both A, B are skew-symmetric or symmetric matrices. Necessary and sufficient conditions for the existence of a (nonsingular) symmetric solution X are formulated in terms of the structured canonical form.


Published in:
Electronic Journal Of Linear Algebra, 26, 215-230
Year:
2013
Publisher:
Pensacola, Int Linear Algebra Soc
ISSN:
1537-9582
Keywords:
Laboratories:




 Record created 2013-10-01, last modified 2018-09-13


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