List questions from matrix-rank

Published on 09 Mar 2026 - 19:01

27

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Speciality of Pivot columns.

Published on 23 Oct 2019 - 14:44

90

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Prove $\mbox{rank} (A − B) = \mbox{rank} (A − AB) + \mbox{rank}(B − AB)$, if $A^2 = A$ and $B^2 = B$

Published on 25 Mar 2026 - 23:11

175

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What is the intuition behind maximizing the smallest nonzero singular value?

Published on 23 Mar 2026 - 3:51

15

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Will $X_{pn}X_{np}'$ be more likely to be invertible when n gets large enough?

Published on 27 Oct 2019 - 8:32

203

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Proving two matrices have equal rank

Published on 28 Oct 2019 - 4:28

376

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Partial derivatives of matrix logarithm

Published on 28 Oct 2019 - 13:44

34

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What conditions could make the commutator $[M^,M] = M^M - MM^*$ full-ranked? $M$ is not normal

Published on 31 Oct 2019 - 1:52

773

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Prove rank(λI−A)=rank((λI−A)^2). Given that A is a diagonalizable matrix and λ an eigenvalue of A.

Published on 01 Nov 2019 - 7:24

208

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Set of Matrices Over Finite Field Whose Pairwise Differences are Invertible

Published on 01 Nov 2019 - 19:12

1.2k

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What is the need for the left null space?

Published on 01 Nov 2019 - 21:27

72

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Find the rank of $A_n$ in terms of $n$

Published on 06 Nov 2019 - 2:31

85

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How to formally calculate the rank of a matrix certain block matrix

Published on 06 Nov 2019 - 9:55

72

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Show that the following matrix is nonsingular

Published on 06 Nov 2019 - 10:13

192

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Diagonalization and rank

Published on 07 Nov 2019 - 17:25

List Question

Rank of circulant matrix with $k$ ones per row

Speciality of Pivot columns.

Prove $\mbox{rank} (A − B) = \mbox{rank} (A − AB) + \mbox{rank}(B − AB)$, if $A^2 = A$ and $B^2 = B$

What is the intuition behind maximizing the smallest nonzero singular value?

Will $X_{pn}X_{np}'$ be more likely to be invertible when n gets large enough?

Proving two matrices have equal rank

Partial derivatives of matrix logarithm

What conditions could make the commutator $[M^,M] = M^M - MM^*$ full-ranked? $M$ is not normal

Prove rank(λI−A)=rank((λI−A)^2). Given that A is a diagonalizable matrix and λ an eigenvalue of A.

Set of Matrices Over Finite Field Whose Pairwise Differences are Invertible

What is the need for the left null space?

Find the rank of $A_n$ in terms of $n$

How to formally calculate the rank of a matrix certain block matrix

Show that the following matrix is nonsingular

Diagonalization and rank

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