Question

Rank of a positive semidefinite block matrix

score 243 · Answer 1 · 2026-03-26 11:00:15

243

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Rank of a positive semidefinite block matrix

Published on 26 Mar 2026 - 11:00

score 53 · Answer 2 · 2020-02-02 01:49:53

53

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In a matrix $A$ $(m\times n)$ ,if $\Bbb{rank}A^T= dim(ker A)$, how to show that A must have an even number of columns?

Published on 02 Feb 2020 - 1:49

score 313 · Answer 3 · 2020-02-02 07:01:59

313

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Prove or disprove the statements about linear map

Published on 02 Feb 2020 - 7:01

score 36 · Answer 4 · 2020-02-02 09:31:58

36

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$k > \operatorname{rank}(A)+\operatorname{rank}(B) \Rightarrow \dim\{Au_1-Bv_1,Au_2-Bv_2,\dots,Au_k-Bv_k\} < k$

Published on 02 Feb 2020 - 9:31

score 103 · Answer 5 · 2026-03-28 11:33:28

103

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When $A$ is $3\times3$, prove that $A^2=0$ iff $A$ has rank less than or equal one and trace zero

Published on 28 Mar 2026 - 11:33

score 42 · Answer 6 · 2020-02-04 11:10:50

42

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What will be the rank of $M$ from the following information?

Published on 04 Feb 2020 - 11:10

score 98 · Answer 7 · 2020-02-05 19:24:38

98

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If A is a square matrix of size n with real entries, with $A = A^{p+1}$, then $rank(A) + rank (I_n - A^p) = n$

Published on 05 Feb 2020 - 19:24

score 118 · Answer 8 · 2026-03-25 07:46:25

118

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$ A^3 + B^2 = I_n $ and $A^5=A^2$, then $\det(A^2 + B^2 + I_n) \geq 0 $ and $\operatorname{rank}(I_n + AB^2) = \mathrm{rank}(I_n - AB^2) $

Published on 25 Mar 2026 - 7:46

score 167 · Answer 9 · 2020-02-09 00:01:05

167

Views

Rank and nullity of matrices

Published on 09 Feb 2020 - 0:01

score 2.5k · Answer 10 · 2020-02-09 06:23:21

2.5k

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Rank of matrix equals dimension of range

Published on 09 Feb 2020 - 6:23

score 126 · Answer 11 · 2026-03-25 06:24:57

126

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Rank of incidence matrix of Hamming graph

Published on 25 Mar 2026 - 6:24

score 213 · Answer 12 · 2020-02-11 17:35:58

213

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Proof: For $A_{m×n}$, $rank(AB)=rank(A)$ if $B$ has rank $n$, $rank(CA)=rank(A)$ if $C$ has rank $n$

Published on 11 Feb 2020 - 17:35

score 37 · Answer 13 · 2020-02-14 18:42:13

37

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The root of the nth matrix

Published on 14 Feb 2020 - 18:42

score 419 · Answer 14 · 2020-02-16 15:59:14

419

Views

Proof that the dimension of the image of a transformation is the rank of the matrix that induces this transformation.

Published on 16 Feb 2020 - 15:59

score 39 · Answer 15 · 2020-02-17 17:37:47

39

Views

eigenvalues of $N$th transpose matrix

Published on 17 Feb 2020 - 17:37

List Question

Rank of a positive semidefinite block matrix

In a matrix $A$ $(m\times n)$ ,if $\Bbb{rank}A^T= dim(ker A)$, how to show that A must have an even number of columns?

Prove or disprove the statements about linear map

$k > \operatorname{rank}(A)+\operatorname{rank}(B) \Rightarrow \dim\{Au_1-Bv_1,Au_2-Bv_2,\dots,Au_k-Bv_k\} < k$

When $A$ is $3\times3$, prove that $A^2=0$ iff $A$ has rank less than or equal one and trace zero

What will be the rank of $M$ from the following information?

If A is a square matrix of size n with real entries, with $A = A^{p+1}$, then $rank(A) + rank (I_n - A^p) = n$

$ A^3 + B^2 = I_n $ and $A^5=A^2$, then $\det(A^2 + B^2 + I_n) \geq 0 $ and $\operatorname{rank}(I_n + AB^2) = \mathrm{rank}(I_n - AB^2) $

Rank and nullity of matrices

Rank of matrix equals dimension of range

Rank of incidence matrix of Hamming graph

Proof: For $A_{m×n}$, $rank(AB)=rank(A)$ if $B$ has rank $n$, $rank(CA)=rank(A)$ if $C$ has rank $n$

The root of the nth matrix

Proof that the dimension of the image of a transformation is the rank of the matrix that induces this transformation.

eigenvalues of $N$th transpose matrix

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