List questions from matrix-rank

Published on 18 Aug 2019 - 14:49

41

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Smallest eigenvalues of $(A-B)'(A-B)$ if $B$ is rank-deficient

Published on 19 Aug 2019 - 15:01

57

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About positive definite matrices

Published on 26 Mar 2026 - 17:11

661

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Dimension of solution space of the the matrix equation AX=0

Published on 23 Aug 2019 - 6:47

76

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How to convert a $3\times 5$ matrix to a product of a $3\times 2$ and $2\times 5$ matrix?

Published on 23 Aug 2019 - 9:39

169

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Maximization of log likelihood wrt $\Sigma_{t}$ subject to $\Sigma_{t}$ is positive definite

Published on 25 Mar 2026 - 23:11

557

Views

$\operatorname{rank} A = \operatorname{rank} A^2$ if and only if $\lim_{\lambda \to 0} (A+\lambda I)^{-1}A$ exists

Published on 25 Aug 2019 - 21:58

163

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Prove that $X'X$ is rank-preserving of X

Published on 27 Aug 2019 - 15:39

77

Views

Product of matrices with equal (full) rank

Published on 27 Aug 2019 - 19:43

335

Views

$\mathrm{rank}(M)=\mathrm{rank}(M^2)$ whenever $M$ is skew-symmetric

Published on 28 Aug 2019 - 8:58

602

Views

Complex Rank and Real Rank of a matrix

Published on 04 Sep 2019 - 9:01

25

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Ensure that a specific matrix decomposition is unique

Published on 04 Sep 2019 - 16:02

114

Views

Taking a subset of rows of full column rank matrix so it becomes square, what happens to rank (and invertibility)?

Published on 12 Sep 2019 - 23:44

314

Views

Intuition behind matrix rank

Published on 13 Sep 2019 - 16:30

117

Views

Is the result $|\text{rank(AB)}-\text{rank(BA)}| \le \text{min}(\text{rank}(A),\text{rank}(B))$

Published on 14 Sep 2019 - 16:16

List Question

Change of basis changes rank of matrix

Smallest eigenvalues of $(A-B)'(A-B)$ if $B$ is rank-deficient

About positive definite matrices

Dimension of solution space of the the matrix equation AX=0

How to convert a $3\times 5$ matrix to a product of a $3\times 2$ and $2\times 5$ matrix?

Maximization of log likelihood wrt $\Sigma_{t}$ subject to $\Sigma_{t}$ is positive definite

$\operatorname{rank} A = \operatorname{rank} A^2$ if and only if $\lim_{\lambda \to 0} (A+\lambda I)^{-1}A$ exists

Prove that $X'X$ is rank-preserving of X

Product of matrices with equal (full) rank

$\mathrm{rank}(M)=\mathrm{rank}(M^2)$ whenever $M$ is skew-symmetric

Complex Rank and Real Rank of a matrix

Ensure that a specific matrix decomposition is unique

Taking a subset of rows of full column rank matrix so it becomes square, what happens to rank (and invertibility)?

Intuition behind matrix rank

Is the result $|\text{rank(AB)}-\text{rank(BA)}| \le \text{min}(\text{rank}(A),\text{rank}(B))$

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