Question

Let A and B are $2 \times 2$ matrices, where AB = BA, show that $\text{A B}^2 = \text{B}^2 \text{A}$

score 725 · Answer 1 · 2017-04-08 11:53:41

725

Views

Let A and B are $2 \times 2$ matrices, where AB = BA, show that $\text{A B}^2 = \text{B}^2 \text{A}$

Published on 08 Apr 2017 - 11:53

score 40 · Answer 2 · 2023-01-30 14:00:09

40

Views

Matrix made up by $2$ orthonormal vectors $x$ and $y$ in $\mathbb{R^2}$ and $y$ is transposed

Published on 30 Jan 2023 - 14:00

score 45 · Answer 3 · 2023-01-31 20:59:13

45

Views

For a square matrix $A$ over any field, does $A^TA=0$ imply $AA^T=0$?

Published on 31 Jan 2023 - 20:59

score 297 · Answer 4 · 2023-02-26 06:22:31

297

Views

When is $A^TA$ invertible?

Published on 26 Feb 2023 - 6:22

score 586 · Answer 5 · 2023-03-06 15:39:23

586

Views

Dot product between two vectors transformed by orthogonal matrices

Published on 06 Mar 2023 - 15:39

score 90 · Answer 6 · 2023-03-14 07:10:33

90

Views

Why a matrix has to be invertible for $\operatorname{adj} A^T=(\operatorname{adj}A)^T$ to be true?

Published on 14 Mar 2023 - 7:10

score 363 · Answer 7 · 2026-03-25 08:09:55

363

Views

Determinant of a matrix is equal to the determinant of its transpose

Published on 25 Mar 2026 - 8:09

score 67 · Answer 8 · 2023-04-04 13:18:01

67

Views

Canonical isomorphism between spaces of endomorphisms

Published on 04 Apr 2023 - 13:18

score 36 · Answer 9 · 2023-04-07 10:29:04

36

Views

Matrix expression of the scalar product between two vectors

Published on 07 Apr 2023 - 10:29

score 76 · Answer 10 · 2023-04-07 14:37:32

76

Views

Dual space and Transposed matrix

Published on 07 Apr 2023 - 14:37

score 114 · Answer 11 · 2026-03-25 11:09:47

114

Views

Prove $\| A\|_2=\|A^T\|_2$

Published on 25 Mar 2026 - 11:09

score 122 · Answer 12 · 2023-04-29 01:12:22

122

Views

Transpose of a linear map given by ODE

Published on 29 Apr 2023 - 1:12

score 131 · Answer 13 · 2023-05-07 14:04:21

131

Views

I am stuck in the evaluation of closed form solution to find $\theta$, why $(X^{T}X)^{-1}X^{T}Y$ is used and not $(XX^{T})$?

Published on 07 May 2023 - 14:04

score 29 · Answer 14 · 2023-05-08 17:12:26

29

Views

What does is mean to center variables?

Published on 08 May 2023 - 17:12

score 118 · Answer 15 · 2023-05-10 20:25:06

118

Views

Is every symmetric matrix in $\mathbb R^n$ a (non-uniform) stretch?

Published on 10 May 2023 - 20:25

List Question

Let A and B are $2 \times 2$ matrices, where AB = BA, show that $\text{A B}^2 = \text{B}^2 \text{A}$

Matrix made up by $2$ orthonormal vectors $x$ and $y$ in $\mathbb{R^2}$ and $y$ is transposed

For a square matrix $A$ over any field, does $A^TA=0$ imply $AA^T=0$?

When is $A^TA$ invertible?

Dot product between two vectors transformed by orthogonal matrices

Why a matrix has to be invertible for $\operatorname{adj} A^T=(\operatorname{adj}A)^T$ to be true?

Determinant of a matrix is equal to the determinant of its transpose

Canonical isomorphism between spaces of endomorphisms

Matrix expression of the scalar product between two vectors

Dual space and Transposed matrix

Prove $\| A\|_2=\|A^T\|_2$

Transpose of a linear map given by ODE

I am stuck in the evaluation of closed form solution to find $\theta$, why $(X^{T}X)^{-1}X^{T}Y$ is used and not $(XX^{T})$?

What does is mean to center variables?

Is every symmetric matrix in $\mathbb R^n$ a (non-uniform) stretch?

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