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Tagged with matrix-congruences matrix-decomposition
4 questions
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Does congruence transformation preserve definiteness of a nonsymmetric matrix?
Let $A$ be a nonsymmetric negative definite matrix, i.e., $x^\top (A+A^\top) x < 0$. If we invoked a congruent transformation, i.e., $DAD^\top=B$ where $D$ is a nonsingular matrix, will the ...
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Interpretation of *congruence for complex matrices
Recently I've been learning *congruence on complex matrix. The definition of *congruence is that:
Let $A, B \in \mathsf{M}_n$. $A$ and $B$ are *-congruent if and only if there exists $S \in \mathsf{M}...
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Question on matrices
Let A be a symmetric matrix of form 2.2 then what should be the elements in matrix B of2.2 such that AB not equals to BA
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