Question

$\text{rank}(A)+\text{rank}(A-I)=n \iff A^2=A$. I don't know my mistake in my proof

score 120 · Answer 1 · 2026-03-26 13:52:17

120

Views

$\text{rank}(A)+\text{rank}(A-I)=n \iff A^2=A$. I don't know my mistake in my proof

Published on 26 Mar 2026 - 13:52

score 36 · Answer 2 · 2023-12-15 01:34:33

36

Views

(Potentially) A Vandermode Matrix Question

Published on 15 Dec 2023 - 1:34

score 97 · Answer 3 · 2023-12-17 12:49:40

97

Views

Inequality about rank of matrix

Published on 17 Dec 2023 - 12:49

score 84 · Answer 4 · 2026-03-25 11:54:16

84

Views

Rank of a matrix with identical diagonal, upper triangle, and lower triangle

Published on 25 Mar 2026 - 11:54

score 22 · Answer 5 · 2023-12-28 03:14:24

22

Views

Closed form error of inner-product-based low-rank approximation of binary matrix

Published on 28 Dec 2023 - 3:14

score 50 · Answer 6 · 2026-03-29 20:21:28

50

Views

Effect of centering rows and columns on the rank of a full rank matrix

Published on 29 Mar 2026 - 20:21

score 45 · Answer 7 · 2024-01-05 23:30:43

45

Views

Existance of matrices such that their left null space contains another matrix with given dimensions

Published on 05 Jan 2024 - 23:30

score 36 · Answer 8 · 2024-01-12 03:35:12

36

Views

Sum of symmetric matrices of rank one

Published on 12 Jan 2024 - 3:35

score 68 · Answer 9 · 2026-02-23 13:46:25

68

Views

Is the set of vectors $(1, 0), (i, 0)$ a linearly independent subset of $\mathbb{C}^2(\mathbb{R})$?

Published on 23 Feb 2026 - 13:46

score 30 · Answer 10 · 2024-01-14 14:54:54

30

Views

Determine the rank of this matrix manually.

Published on 14 Jan 2024 - 14:54

score 71 · Answer 11 · 2024-01-15 22:16:59

71

Views

Prove that if $R(T)\cap N(T)=\{0\}$ then $\operatorname{rank}(T)=\operatorname{rank}(T^2)$

Published on 15 Jan 2024 - 22:16

score 35 · Answer 12 · 2026-03-25 17:33:51

35

Views

From adjacency Matrix can we find the maximum number of disjoint matching pairs of a simple undirected graph?

Published on 25 Mar 2026 - 17:33

score 44 · Answer 13 · 2024-01-17 17:20:46

44

Views

If $\begin{bmatrix}XY \\ X\end{bmatrix}$ has full column rank, then does $X$ have full column rank?

Published on 17 Jan 2024 - 17:20

score 127 · Answer 14 · 2024-01-18 11:57:59

127

Views

Rank 1 matrix with given anti-diagonal sums

Published on 18 Jan 2024 - 11:57

score 67 · Answer 15 · 2024-01-19 01:17:45

67

Views

row rank = column rank over a PID?

Published on 19 Jan 2024 - 1:17

List Question

$\text{rank}(A)+\text{rank}(A-I)=n \iff A^2=A$. I don't know my mistake in my proof

(Potentially) A Vandermode Matrix Question

Inequality about rank of matrix

Rank of a matrix with identical diagonal, upper triangle, and lower triangle

Closed form error of inner-product-based low-rank approximation of binary matrix

Effect of centering rows and columns on the rank of a full rank matrix

Existance of matrices such that their left null space contains another matrix with given dimensions

Sum of symmetric matrices of rank one

Is the set of vectors $(1, 0), (i, 0)$ a linearly independent subset of $\mathbb{C}^2(\mathbb{R})$?

Determine the rank of this matrix manually.

Prove that if $R(T)\cap N(T)=\{0\}$ then $\operatorname{rank}(T)=\operatorname{rank}(T^2)$

From adjacency Matrix can we find the maximum number of disjoint matching pairs of a simple undirected graph?

If $\begin{bmatrix}XY \\ X\end{bmatrix}$ has full column rank, then does $X$ have full column rank?

Rank 1 matrix with given anti-diagonal sums

row rank = column rank over a PID?

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