Question

Relating spactra of matrices that are connected by a rectangular orthogonal transformation.

score 33 · Answer 1 · 2021-10-09 22:37:02

33

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Relating spactra of matrices that are connected by a rectangular orthogonal transformation.

Published on 09 Oct 2021 - 22:37

score 719 · Answer 2 · 2021-10-17 16:29:33

719

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Conjugacy classes of the orthogonal group $O(2)$

Published on 17 Oct 2021 - 16:29

score 40 · Answer 3 · 2021-10-21 01:42:59

40

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A question about two orthonormal vectors

Published on 21 Oct 2021 - 1:42

score 171 · Answer 4 · 2021-10-22 19:54:02

171

Views

Let A be an $n \times k$ matrix with $W$ as the column space. Show that the solution space of $A(A^T) x = 0$ is given by $W^⊥$.

Published on 22 Oct 2021 - 19:54

score 131 · Answer 5 · 2021-10-28 03:33:14

131

Views

Let $\{U_i\}_{i=1}^k, U_i\in\mathbb R^{n\times n}$ be orthogonal matrices. Show that the product $U = U_1U_2\cdots U_k$

Published on 28 Oct 2021 - 3:33

score 1k · Answer 6 · 2021-10-28 11:38:54

1k

Views

Suppose $P$ and $Q$ are orthogonal projections and $P+Q = I$. Prove that $P-Q$ must be an orthogonal matrix.

Published on 28 Oct 2021 - 11:38

score 103 · Answer 7 · 2021-10-28 18:33:03

103

Views

Classical vs Modified Gram-Schmidt

Published on 28 Oct 2021 - 18:33

score 97 · Answer 8 · 2021-10-29 12:15:11

97

Views

Verify that if $A\in\mathbb R^{m\times n}_n$, then $A^+ = R^{-1}Q_1^T$.

Published on 29 Oct 2021 - 12:15

score 344 · Answer 9 · 2021-10-29 16:56:03

344

Views

Proving the limit of any convergent sequence of orthogonal matrices is again an orthogonal matrix

Published on 29 Oct 2021 - 16:56

score 303 · Answer 10 · 2021-10-29 22:35:45

303

Views

Give (in terms of orthonormal basis ) a vector in a given Span

Published on 29 Oct 2021 - 22:35

score 145 · Answer 11 · 2021-11-04 20:10:13

145

Views

Proof involving orthogonally diagonalizable matrix

Published on 04 Nov 2021 - 20:10

score 153 · Answer 12 · 2021-11-08 13:49:34

153

Views

Orthogonal matrix and trigonometric functions of matrices

Published on 08 Nov 2021 - 13:49

score 48 · Answer 13 · 2021-11-08 16:33:42

48

Views

Stationary points of a function defined on a manifold

Published on 08 Nov 2021 - 16:33

score 90 · Answer 14 · 2026-03-25 08:13:44

90

Views

Construction of an Orthogonal matrix to reorder diagonal blocks of real Schur form of a matrix

Published on 25 Mar 2026 - 8:13

score 84 · Answer 15 · 2021-11-10 18:24:41

84

Views

Is congruent diagonalization of symmetric matrix necessarily a similar one?

Published on 10 Nov 2021 - 18:24

List Question

Relating spactra of matrices that are connected by a rectangular orthogonal transformation.

Conjugacy classes of the orthogonal group $O(2)$

A question about two orthonormal vectors

Let A be an $n \times k$ matrix with $W$ as the column space. Show that the solution space of $A(A^T) x = 0$ is given by $W^⊥$.

Let $\{U_i\}_{i=1}^k, U_i\in\mathbb R^{n\times n}$ be orthogonal matrices. Show that the product $U = U_1U_2\cdots U_k$

Suppose $P$ and $Q$ are orthogonal projections and $P+Q = I$. Prove that $P-Q$ must be an orthogonal matrix.

Classical vs Modified Gram-Schmidt

Verify that if $A\in\mathbb R^{m\times n}_n$, then $A^+ = R^{-1}Q_1^T$.

Proving the limit of any convergent sequence of orthogonal matrices is again an orthogonal matrix

Give (in terms of orthonormal basis ) a vector in a given Span

Proof involving orthogonally diagonalizable matrix

Orthogonal matrix and trigonometric functions of matrices

Stationary points of a function defined on a manifold

Construction of an Orthogonal matrix to reorder diagonal blocks of real Schur form of a matrix

Is congruent diagonalization of symmetric matrix necessarily a similar one?

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