Question

Let $T$ be a normal operator on a finite-dimensional complex inner product space. Show that if T is a projection, then it is an orthogonal projection.

score 391 · Answer 1 · 2026-03-24 22:07:44

391

Views

Let $T$ be a normal operator on a finite-dimensional complex inner product space. Show that if T is a projection, then it is an orthogonal projection.

Published on 24 Mar 2026 - 22:07

score 1k · Answer 2 · 2026-03-26 09:38:15

1k

Views

Finding a presentation matrix for an $F[t]$-module

Published on 26 Mar 2026 - 9:38

score 39 · Answer 3 · 2018-04-06 20:07:28

39

Views

How would I factor this equation that was calculated as the determinant of a matrix?

Published on 06 Apr 2018 - 20:07

score 135 · Answer 4 · 2026-04-12 00:46:51

135

Views

What is the rank of a matrix when the difference between its rows is same?

Published on 12 Apr 2026 - 0:46

score 100 · Answer 5 · 2026-03-28 10:04:41

100

Views

$A$ is an $n \times n$ diagonalizable matrix with exactly $k$ non-zero eigenvalues, find a basis for $Range(L)$

Published on 28 Mar 2026 - 10:04

score 1.6k · Answer 6 · 2018-04-06 20:58:06

1.6k

Views

Proving that a multivariable function is surjective?

Published on 06 Apr 2018 - 20:58

score 93 · Answer 7 · 2026-04-12 06:43:51

93

Views

w = RsR', solve for R where w, s are known, symmetric and PD. R is orthogonal with det(R)=1

Published on 12 Apr 2026 - 6:43

score 162 · Answer 8 · 2026-04-12 09:31:53

162

Views

Sum and difference of projectors

Published on 12 Apr 2026 - 9:31

score 576 · Answer 9 · 2026-04-08 18:35:55

576

Views

Implementation of quaternion coordinate transformation

Published on 08 Apr 2026 - 18:35

score 1.4k · Answer 10 · 2026-04-12 06:08:24

1.4k

Views

Shortest Distance between two lines in the 3D plane

Published on 12 Apr 2026 - 6:08

score 60 · Answer 11 · 2026-04-10 09:52:59

60

Views

I need help getting started with this one please (confusing Advanced Linear Algebra Problem)

Published on 10 Apr 2026 - 9:52

score 374 · Answer 12 · 2026-03-25 17:42:07

374

Views

Let $T$ be a self-adjoint operator on $V$ where $\beta$ is a basis for $V$. The matrix of $T$ is Hermitian if and only if $\beta$ is orthonormal.

Published on 25 Mar 2026 - 17:42

score 107 · Answer 13 · 2026-04-10 22:20:08

107

Views

How do I get this matrix in Smith Normal Form? Every matrix in $M(\mathbb{Z})$ can be taked in Smith form?

Published on 10 Apr 2026 - 22:20

score 66 · Answer 14 · 2026-03-27 14:51:40

66

Views

(Vectors) Is there an origin O so that OP1+OP2 = OP3?

Published on 27 Mar 2026 - 14:51

score 29 · Answer 15 · 2026-04-09 02:18:01

29

Views

Showing inclusion of multivariable function

Published on 09 Apr 2026 - 2:18

List Question

Let $T$ be a normal operator on a finite-dimensional complex inner product space. Show that if T is a projection, then it is an orthogonal projection.

Finding a presentation matrix for an $F[t]$-module

How would I factor this equation that was calculated as the determinant of a matrix?

What is the rank of a matrix when the difference between its rows is same?

$A$ is an $n \times n$ diagonalizable matrix with exactly $k$ non-zero eigenvalues, find a basis for $Range(L)$

Proving that a multivariable function is surjective?

w = RsR', solve for R where w, s are known, symmetric and PD. R is orthogonal with det(R)=1

Sum and difference of projectors

Implementation of quaternion coordinate transformation

Shortest Distance between two lines in the 3D plane

I need help getting started with this one please (confusing Advanced Linear Algebra Problem)

Let $T$ be a self-adjoint operator on $V$ where $\beta$ is a basis for $V$. The matrix of $T$ is Hermitian if and only if $\beta$ is orthonormal.

How do I get this matrix in Smith Normal Form? Every matrix in $M(\mathbb{Z})$ can be taked in Smith form?

(Vectors) Is there an origin O so that OP1+OP2 = OP3?

Showing inclusion of multivariable function

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