Question

Show that for every vector $c \in \Bbb{R}^n$, the vector $A^T(AA^T)^{-1}Ac$ is orthogonal to the null space of the matrix $A$.

score 57 · Answer 1 · 2026-03-25 23:42:39

57

Views

Show that for every vector $c \in \Bbb{R}^n$, the vector $A^T(AA^T)^{-1}Ac$ is orthogonal to the null space of the matrix $A$.

Published on 25 Mar 2026 - 23:42

score 107 · Answer 2 · 2026-04-09 02:21:51

107

Views

$\lambda = \max_{\mathbf{x}}\frac{\mathbf{x}^{T}\mathbf{A}\mathbf{x}}{\mathbf{x}^{T}\mathbf{x}}$ for non-negative matrices $A$?

Published on 09 Apr 2026 - 2:21

score 26 · Answer 3 · 2018-04-05 20:07:42

26

Views

Tupel of lineary independent linear forms gives a surjection

Published on 05 Apr 2018 - 20:07

score 45 · Answer 4 · 2026-04-11 00:12:15

45

Views

Eigenvectors of Period-translation matrix for Hill's equation

Published on 11 Apr 2026 - 0:12

score 34 · Answer 5 · 2026-04-10 09:25:29

34

Views

Picking two pivot columns

Published on 10 Apr 2026 - 9:25

score 618 · Answer 6 · 2026-03-26 16:56:38

618

Views

Prove that the column vectors of a $n \times n$ matrix are a basis for $\mathbb{F}^n$ if and only if $\det X \neq 0.$

Published on 26 Mar 2026 - 16:56

score 588 · Answer 7 · 2018-04-05 21:10:31

588

Views

Determine if the sets of vectors are a basis for the indicated space

Published on 05 Apr 2018 - 21:10

score 123 · Answer 8 · 2026-03-28 10:03:56

123

Views

Find all eigenvalues for $L(\vec{x})=\vec{x}-2proj_\vec{n}(\vec{x})$ for some non-zero vector $\vec{n}$

Published on 28 Mar 2026 - 10:03

score 1.5k · Answer 9 · 2026-04-12 04:02:21

1.5k

Views

How to prove that a subset is a partition?

Published on 12 Apr 2026 - 4:02

score 45 · Answer 10 · 2026-03-27 14:45:28

45

Views

Ratio of two unknown line segments using known side

Published on 27 Mar 2026 - 14:45

score 836 · Answer 11 · 2026-03-25 07:46:04

836

Views

If $A$ is idempotent then $A$ is similar to a diagonal matrix with only $0$'s and $1$'s on the diagonal.

Published on 25 Mar 2026 - 7:46

score 116 · Answer 12 · 2026-03-27 14:57:41

116

Views

a result from rank-nullity theorem

Published on 27 Mar 2026 - 14:57

score 69 · Answer 13 · 2026-04-12 00:22:14

69

Views

How to calculate $\frac{\partial\|A(I_n\otimes B)x\|^2}{\partial B}$?

Published on 12 Apr 2026 - 0:22

score 29 · Answer 14 · 2026-04-12 02:11:36

29

Views

Linear Algebra-Orthogonal Vectors

Published on 12 Apr 2026 - 2:11

score 3.3k · Answer 15 · 2026-03-28 23:59:41

3.3k

Views

Dimension of the space of linear operators on a finite vector space

Published on 28 Mar 2026 - 23:59

List Question

Show that for every vector $c \in \Bbb{R}^n$, the vector $A^T(AA^T)^{-1}Ac$ is orthogonal to the null space of the matrix $A$.

$\lambda = \max_{\mathbf{x}}\frac{\mathbf{x}^{T}\mathbf{A}\mathbf{x}}{\mathbf{x}^{T}\mathbf{x}}$ for non-negative matrices $A$?

Tupel of lineary independent linear forms gives a surjection

Eigenvectors of Period-translation matrix for Hill's equation

Picking two pivot columns

Prove that the column vectors of a $n \times n$ matrix are a basis for $\mathbb{F}^n$ if and only if $\det X \neq 0.$

Determine if the sets of vectors are a basis for the indicated space

Find all eigenvalues for $L(\vec{x})=\vec{x}-2proj_\vec{n}(\vec{x})$ for some non-zero vector $\vec{n}$

How to prove that a subset is a partition?

Ratio of two unknown line segments using known side

If $A$ is idempotent then $A$ is similar to a diagonal matrix with only $0$'s and $1$'s on the diagonal.

a result from rank-nullity theorem

How to calculate $\frac{\partial\|A(I_n\otimes B)x\|^2}{\partial B}$?

Linear Algebra-Orthogonal Vectors

Dimension of the space of linear operators on a finite vector space

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