Question

$\begin{bmatrix}\mathbf O & U\\ V^T & 0\end{bmatrix}$ is diagonalizable?

score 145 · Answer 1 · 2022-07-26 06:04:57

145

Views

$\begin{bmatrix}\mathbf O & U\\ V^T & 0\end{bmatrix}$ is diagonalizable?

Published on 26 Jul 2022 - 6:04

score 202 · Answer 2 · 2022-07-27 10:02:28

202

Views

Proof that $\textbf{Q} = \textbf{I}_n - \textbf{X}(\textbf{X}^T\textbf{X})^{-1}\textbf{X}^T$ is of rank $n-k-1$.

Published on 27 Jul 2022 - 10:02

score 204 · Answer 3 · 2022-08-02 14:06:49

204

Views

Rank of matrix with $0$s and $1$s over finite field $\mathbb{F}_2$ and ring $\mathbb{Z}_q$

Published on 02 Aug 2022 - 14:06

score 149 · Answer 4 · 2022-08-03 15:56:02

149

Views

What is the dimension of the subspace $S$ of the vector space of all $8×10$ matrices?

Published on 03 Aug 2022 - 15:56

score 26 · Answer 5 · 2022-08-04 16:02:23

26

Views

Matrix valued function with low-rank input matrix

Published on 04 Aug 2022 - 16:02

score 39 · Answer 6 · 2022-08-05 21:22:26

39

Views

On the rank of a submatrix

Published on 05 Aug 2022 - 21:22

score 34 · Answer 7 · 2026-03-25 16:01:14

34

Views

How does $\text{rank}(A)$ relate to $\text{rank}(\text{Diag}(\text{Vec}(A)))$?

Published on 25 Mar 2026 - 16:01

score 50 · Answer 8 · 2022-08-18 01:16:43

50

Views

$A^k$ and nonzero elements

Published on 18 Aug 2022 - 1:16

score 73 · Answer 9 · 2022-08-25 12:50:26

73

Views

Show that Rows are linearly dependent

Published on 25 Aug 2022 - 12:50

score 27 · Answer 10 · 2022-08-25 14:03:12

27

Views

$B\in\mathbb{R}^{n\times n}$ has $n$ different rows and $\operatorname{rank} B = n-1$. Is any selection of $n-1$ rows of $B$ linearly independent?

Published on 25 Aug 2022 - 14:03

score 49 · Answer 11 · 2022-08-25 15:52:16

49

Views

Let $v_1,\ldots, v_n$ be linear independent vectors and $v$ a linear combination of those. Are $v_1-v,\ldots, v_n-v$ still linear independent?

Published on 25 Aug 2022 - 15:52

score 108 · Answer 12 · 2022-08-26 10:28:15

108

Views

How do I prove the statement "If det() = 7, then = 0 has only the trivial solution"?

Published on 26 Aug 2022 - 10:28

score 50 · Answer 13 · 2022-08-27 23:12:55

50

Views

Rank of non-singular matrix post multiplied by a singular matrix

Published on 27 Aug 2022 - 23:12

score 38 · Answer 14 · 2022-08-30 20:24:09

38

Views

If rank(XY) = rank(X), show that the column space C(XY) = C(X)

Published on 30 Aug 2022 - 20:24

score 55 · Answer 15 · 2022-09-01 09:29:21

55

Views

If a matrix has rank r, show that there exists two matrices such that their product give initial matrix, both with rank r

Published on 01 Sep 2022 - 9:29

List Question

$\begin{bmatrix}\mathbf O & U\\ V^T & 0\end{bmatrix}$ is diagonalizable?

Proof that $\textbf{Q} = \textbf{I}_n - \textbf{X}(\textbf{X}^T\textbf{X})^{-1}\textbf{X}^T$ is of rank $n-k-1$.

Rank of matrix with $0$s and $1$s over finite field $\mathbb{F}_2$ and ring $\mathbb{Z}_q$

What is the dimension of the subspace $S$ of the vector space of all $8×10$ matrices?

Matrix valued function with low-rank input matrix

On the rank of a submatrix

How does $\text{rank}(A)$ relate to $\text{rank}(\text{Diag}(\text{Vec}(A)))$?

$A^k$ and nonzero elements

Show that Rows are linearly dependent

$B\in\mathbb{R}^{n\times n}$ has $n$ different rows and $\operatorname{rank} B = n-1$. Is any selection of $n-1$ rows of $B$ linearly independent?

Let $v_1,\ldots, v_n$ be linear independent vectors and $v$ a linear combination of those. Are $v_1-v,\ldots, v_n-v$ still linear independent?

How do I prove the statement "If det() = 7, then = 0 has only the trivial solution"?

Rank of non-singular matrix post multiplied by a singular matrix

If rank(XY) = rank(X), show that the column space C(XY) = C(X)

If a matrix has rank r, show that there exists two matrices such that their product give initial matrix, both with rank r

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