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Discrete version of Sylvester's Law of Inertia

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#matrices #reference-request #matrix-congruences
51
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Question on matrices

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#matrix-equations #matrix-calculus #matrix-decomposition #mathematicians #matrix-congruences
96
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prove that a antisymmetric and invertible matrix is congruent to another matrix

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#matrices #matrix-congruences
525
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Does congruence preserve the reality of matrix eigenvalues?

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#matrices #eigenvalues-eigenvectors #matrix-congruences
217
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What happens when two diagonal matrices are unitarily similar?

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#matrices #matrix-congruences
560
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eigenvalues of a matrix and its product with a diagonal matrix

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#linear-algebra #matrices #eigenvalues-eigenvectors #matrix-congruences
826
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Congruent matrices - why do we require invertiblility?

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#linear-algebra #matrices #inverse #matrix-congruences
1.3k
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Two real symmetric matrices are congruent if and only if they have the same rank and signature.

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#linear-algebra #matrix-congruences
1k
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What are the properties of congruent classes over symmetric matrices?

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#linear-algebra #symmetric-matrices #congruence-relations #matrix-congruences
189
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Check if there exists an orthogonal matrix $P$ such that $B=P^{-1}AP$

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#linear-algebra #bilinear-form #matrix-congruences
69
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How to show if a non-(skew) symmetric matrix is congruent/orthogonal equivalent to a diagonal matrix

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#matrices #matrix-congruences
625
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Congruence transformation of symmetric matrices

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#linear-algebra #symmetric-matrices #matrix-congruences
91
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$A ^3$ is congruent to $A$ for a singular symmetric real matrix $A$

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#matrices #symmetric-matrices #matrix-congruences
32
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Congruently and Hermitely diagonalisable matrices

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#linear-algebra #diagonalization #bilinear-form #matrix-congruences #sesquilinear-forms
1.1k
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Did I just discover a new way to calculate the signature of a matrix?

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#linear-algebra #matrices #algebra-precalculus #symmetric-matrices #matrix-congruences

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