Question

Orthogonal complement of $\operatorname{im}(A)$

score 84 · Answer 1 · 2019-07-10 16:28:01

84

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Orthogonal complement of $\operatorname{im}(A)$

Published on 10 Jul 2019 - 16:28

score 63 · Answer 2 · 2019-07-11 20:40:52

63

Views

Bounding/Finding all values for the rank of a matrix

Published on 11 Jul 2019 - 20:40

score 55 · Answer 3 · 2019-07-11 22:24:17

55

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Similar matrix $B$ to a matrix $A$ with rank of $1$

Published on 11 Jul 2019 - 22:24

score 529 · Answer 4 · 2019-07-11 23:51:18

529

Views

Prove rank(A) = rank($A^T$) by using orthogonal complement of image space of A

Published on 11 Jul 2019 - 23:51

score 756 · Answer 5 · 2019-07-12 09:06:56

756

Views

How does the rank of matrix affects solvability of $Ax = b$?

Published on 12 Jul 2019 - 9:06

score 711 · Answer 6 · 2019-07-13 02:44:01

711

Views

If A is an $n\times n$ square matrix such that $A^3=A$ , then show that $\operatorname{rank}(A) + \operatorname{tr}(A)$ is even

Published on 13 Jul 2019 - 2:44

score 198 · Answer 7 · 2019-07-14 13:23:16

198

Views

Let $K$ be a field and $A \in K^{n \times n}$, $A^2=0$. Show that $\operatorname{rank}(A) \leq \frac{n}{2}$.

Published on 14 Jul 2019 - 13:23

score 502 · Answer 8 · 2019-07-18 13:27:07

502

Views

Proving $\operatorname{rank}A =\operatorname{rank}B$ when $AB = 2A + 3B$

Published on 18 Jul 2019 - 13:27

score 65 · Answer 9 · 2019-07-20 11:43:52

65

Views

rank of $A = (a_{ij}) \in \mathbb{R}^{n \times n}$ where $a_{ij} := i +j \quad \forall 1 \leq i, j \leq n$.

Published on 20 Jul 2019 - 11:43

score 74 · Answer 10 · 2019-07-20 13:30:38

74

Views

Let $T\in Mat_{m\times n}(\mathbb{R}), X\in Mat_{n\times p}(\mathbb{R})$. Given the subspace $S=\{X|TX=0\}$, Find $dimS$

Published on 20 Jul 2019 - 13:30

score 3.9k · Answer 11 · 2019-07-22 21:56:12

3.9k

Views

What is Rank, Nullity, Range, and Kernel in relation to each other.

Published on 22 Jul 2019 - 21:56

score 92 · Answer 12 · 2019-07-23 21:03:47

92

Views

Use Rank Nullity Theorem

Published on 23 Jul 2019 - 21:03

score 754 · Answer 13 · 2019-07-25 10:51:50

754

Views

Show that rank($AQ$) = rank($A$)

Published on 25 Jul 2019 - 10:51

score 110 · Answer 14 · 2019-07-27 06:08:07

110

Views

How to show the matrix has Rank $\le 5$

Published on 27 Jul 2019 - 6:08

score 49 · Answer 15 · 2019-07-28 10:55:12

49

Views

Is $L_B$ onto if $B$ is an $n$ by $p$ matrix with $\operatorname{rank}(B)=n$?

Published on 28 Jul 2019 - 10:55

List Question

Orthogonal complement of $\operatorname{im}(A)$

Bounding/Finding all values for the rank of a matrix

Similar matrix $B$ to a matrix $A$ with rank of $1$

Prove rank(A) = rank($A^T$) by using orthogonal complement of image space of A

How does the rank of matrix affects solvability of $Ax = b$?

If A is an $n\times n$ square matrix such that $A^3=A$ , then show that $\operatorname{rank}(A) + \operatorname{tr}(A)$ is even

Let $K$ be a field and $A \in K^{n \times n}$, $A^2=0$. Show that $\operatorname{rank}(A) \leq \frac{n}{2}$.

Proving $\operatorname{rank}A =\operatorname{rank}B$ when $AB = 2A + 3B$

rank of $A = (a_{ij}) \in \mathbb{R}^{n \times n}$ where $a_{ij} := i +j \quad \forall 1 \leq i, j \leq n$.

Let $T\in Mat_{m\times n}(\mathbb{R}), X\in Mat_{n\times p}(\mathbb{R})$. Given the subspace $S=\{X|TX=0\}$, Find $dimS$

What is Rank, Nullity, Range, and Kernel in relation to each other.

Use Rank Nullity Theorem

Show that rank($AQ$) = rank($A$)

How to show the matrix has Rank $\le 5$

Is $L_B$ onto if $B$ is an $n$ by $p$ matrix with $\operatorname{rank}(B)=n$?

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