Structured canonical forms for products of ( skew - ) symmetric matrices and the matrix equation XAX =
نویسندگان
چکیده
The contragredient transformation A 7→ P−1AP−T, B 7→ PTBP 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.
منابع مشابه
Structured canonical forms for products of (skew-) symmetric matrices and the matrix equation XAX=B
The contragredient transformation A 7→ PAP, B 7→ PBP 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 matri...
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The contragredient transformation A 7→ PAP, B 7→ PBP 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 matri...
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