Question

How can we have a complex basis for a real-valued space?

score 42 · Answer 1 · 2026-03-25 14:20:55

42

Views

How can we have a complex basis for a real-valued space?

Published on 25 Mar 2026 - 14:20

score 1k · Answer 2 · 2018-09-03 02:43:38

1k

Views

How to prove that the range of orthogonal projection matrix $P=A(A^HA)^{-1}A^H$ is the same as $R(A)$?

Published on 03 Sep 2018 - 2:43

score 168 · Answer 3 · 2018-09-03 16:15:08

168

Views

Inner product - Show that there is a unique vector

Published on 03 Sep 2018 - 16:15

score 73 · Answer 4 · 2026-03-26 04:31:21

73

Views

Showing $\langle Ku,v\rangle=\langle u,K^*v\rangle$ for a Fredholm Operator $K$

Published on 26 Mar 2026 - 4:31

score 379 · Answer 5 · 2026-03-25 15:43:40

379

Views

If $a\cdot b=a \cdot c$, what is the relationship between $b$ and $c$? $a$, $b$, and $c$ are all vectors.

Published on 25 Mar 2026 - 15:43

score 827 · Answer 6 · 2026-03-30 09:50:32

827

Views

Scalar(inner) product of polynomial and norm

Published on 30 Mar 2026 - 9:50

score 92 · Answer 7 · 2026-03-25 07:43:05

92

Views

Prove the identity in inner product space

Published on 25 Mar 2026 - 7:43

score 66 · Answer 8 · 2018-09-10 20:51:04

66

Views

Let $V$ be an inner prod. sp. and $W$ be its finite dim. linear subspace w/ orthonormal basis $\left\{w_1,\dots,w_n\right\}$

Published on 10 Sep 2018 - 20:51

score 46 · Answer 9 · 2026-03-26 04:31:58

46

Views

Determining the adjoint of $S(\sum_{i=1}^n \alpha_i e_i) = \alpha_2 e_1 - \alpha_1 e_2$.

Published on 26 Mar 2026 - 4:31

score 121 · Answer 10 · 2026-03-25 15:41:20

121

Views

Compatibility of cross and inner product on $\mathbb{R}^3$

Published on 25 Mar 2026 - 15:41

score 1.1k · Answer 11 · 2026-03-25 15:38:56

1.1k

Views

Difference between dot product and cross product

Published on 25 Mar 2026 - 15:38

score 86 · Answer 12 · 2026-04-01 12:50:03

86

Views

Properties of matrix of linear transformation w.r.t an orthonormal basis

Published on 01 Apr 2026 - 12:50

score 925 · Answer 13 · 2026-03-25 09:26:10

925

Views

$T$ is an isometry if and only if $\langle Tx, Ty \rangle = \langle x, y \rangle$

Published on 25 Mar 2026 - 9:26

score 67 · Answer 14 · 2026-03-27 17:23:49

67

Views

Representation of Lie group

Published on 27 Mar 2026 - 17:23

score 1.4k · Answer 15 · 2026-03-27 05:58:03

1.4k

Views

Show Cauchy-Schwarz inequality from triangle inequality for $\mathbb{C}$-vector space

Published on 27 Mar 2026 - 5:58

List Question

How can we have a complex basis for a real-valued space?

How to prove that the range of orthogonal projection matrix $P=A(A^HA)^{-1}A^H$ is the same as $R(A)$?

Inner product - Show that there is a unique vector

Showing $\langle Ku,v\rangle=\langle u,K^*v\rangle$ for a Fredholm Operator $K$

If $a\cdot b=a \cdot c$, what is the relationship between $b$ and $c$? $a$, $b$, and $c$ are all vectors.

Scalar(inner) product of polynomial and norm

Prove the identity in inner product space

Let $V$ be an inner prod. sp. and $W$ be its finite dim. linear subspace w/ orthonormal basis $\left\{w_1,\dots,w_n\right\}$

Determining the adjoint of $S(\sum_{i=1}^n \alpha_i e_i) = \alpha_2 e_1 - \alpha_1 e_2$.

Compatibility of cross and inner product on $\mathbb{R}^3$

Difference between dot product and cross product

Properties of matrix of linear transformation w.r.t an orthonormal basis

$T$ is an isometry if and only if $\langle Tx, Ty \rangle = \langle x, y \rangle$

Representation of Lie group

Show Cauchy-Schwarz inequality from triangle inequality for $\mathbb{C}$-vector space

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