List questions from matrix-rank

Published on 11 Apr 2018 - 5:24

47

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$\operatorname{rank}(A)=n$ then $\left\lVert{A(A^TA)^{-1}A^T}\right\rVert_2 = 1$

Published on 15 Apr 2018 - 17:12

3k

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Show the rank of A equals to the number of non-zero eigenvalues of $A^TA$

Published on 18 Apr 2018 - 3:54

488

Views

Can the limit of a sequence of matrices of fixed rank have higher rank?

Published on 18 Apr 2018 - 14:14

77

Views

how to prove this Theorem null matrix?

Published on 19 Apr 2018 - 3:37

29

Views

Matrix of random variables

Published on 19 Apr 2018 - 9:22

64

Views

Proving numerically that the rank of a matrix has a certain value

Published on 20 Apr 2018 - 13:07

753

Views

Linear Algebra Solution Types Proven with Rank

Published on 21 Apr 2018 - 6:10

619

Views

Vector space of matrices of rank $\le r$

Published on 22 Apr 2018 - 23:50

173

Views

Nuclear norm and Schatten norm in practice

Published on 17 Mar 2026 - 5:20

417

Views

Uniqueness of trace as linearization of the rank

Published on 27 Apr 2018 - 15:09

78

Views

What is the rank of $B$?

Published on 22 Mar 2026 - 7:39

438

Views

$\text{rk}(AB)=\text{rk}(BA)$ generally

Published on 30 Apr 2018 - 13:57

13.3k

Views

Why is the nullity of an invertible matrix 0?

Published on 30 Apr 2018 - 14:58

1.4k

Views

How to prove for a PSD matrix $ \lambda _{\min} (A)\operatorname{tr}(B)\le \operatorname{tr}(AB) \le \lambda _{\max} (A)\operatorname{tr}(B)$

Published on 03 May 2018 - 16:39

List Question

Question About Definition for the Rank of a Matrix

$\operatorname{rank}(A)=n$ then $\left\lVert{A(A^TA)^{-1}A^T}\right\rVert_2 = 1$

Show the rank of A equals to the number of non-zero eigenvalues of $A^TA$

Can the limit of a sequence of matrices of fixed rank have higher rank?

how to prove this Theorem null matrix?

Matrix of random variables

Proving numerically that the rank of a matrix has a certain value

Linear Algebra Solution Types Proven with Rank

Vector space of matrices of rank $\le r$

Nuclear norm and Schatten norm in practice

Uniqueness of trace as linearization of the rank

What is the rank of $B$?

$\text{rk}(AB)=\text{rk}(BA)$ generally

Why is the nullity of an invertible matrix 0?

How to prove for a PSD matrix $ \lambda _{\min} (A)\operatorname{tr}(B)\le \operatorname{tr}(AB) \le \lambda _{\max} (A)\operatorname{tr}(B)$

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