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Does congruence transformation preserve definiteness of a nonsymmetric matrix?

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#linear-algebra #matrix-decomposition #positive-definite #congruence-relations #matrix-congruences
79
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Proof that any antisymmetric matrix C is congruent to a block diagonal matrix?

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#jordan-normal-form #symmetric-matrices #matrix-congruences
3.5k
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If $AA^T$ is a diagonal matrix, what can be said about $A^TA$?

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#linear-algebra #matrices #matrix-congruences
990
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Number of distinct equivalence classes under *-congruence and T-congruence

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#linear-algebra #matrices #eigenvalues-eigenvectors #equivalence-relations #matrix-congruences
768
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Show that congruence of matrices is an equivalence relation.

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#linear-algebra #equivalence-relations #matrix-congruences
993
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How to solve system of linear congruences with the same modulo?

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#modular-arithmetic #matrix-congruences
66
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Square root of a matrix $A$ and matrices similar to $A$

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#matrix-analysis #matrix-congruences
54
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Similarity of matrices and its square root over $\mathbb Z$

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#matrix-analysis #matrix-congruences
45
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Square root and similarity between integer matrices

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#matrix-equations #matrix-analysis #matrix-congruences
66
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Square root of a specific matrix over $\Bbb Z$

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#matrix-equations #matrix-analysis #matrix-congruences
102
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Kronecker-Weierstrass problem, 3x6 matrices conjugacy or congruent classes?

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#linear-algebra #diagonalization #jordan-normal-form #congruence-relations #matrix-congruences
1.4k
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Is every skew-symmetric matrix congruent to a diagonal matrix?

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#linear-algebra #matrix-congruences
799
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Diagonalizing a bilinear form

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#linear-algebra #bilinear-form #matrix-congruences
1.3k
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How to reduce a quadric into canonical form without rigorous calculations?

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#linear-algebra #linear-transformations #quadratic-forms #quadrics #matrix-congruences
173
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How to find the normal form under congruence of the given matrix.

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

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