Question

Does $Ax+Bx=\lambda x$ imply $\langle Ax ,x \rangle + \langle Bx, x \rangle=\langle\lambda x, x \rangle$?

score 82 · Answer 1 · 2026-04-14 16:38:25

82

Views

Does $Ax+Bx=\lambda x$ imply $\langle Ax ,x \rangle + \langle Bx, x \rangle=\langle\lambda x, x \rangle$?

Published on 14 Apr 2026 - 16:38

score 63 · Answer 2 · 2026-04-15 01:10:56

63

Views

An alternative proof of Mashke's theorem for a case $K=\mathbb C$ or $K$ is a subfield of $\mathbb C$

Published on 15 Apr 2026 - 1:10

score 106 · Answer 3 · 2026-04-14 00:52:36

106

Views

Why are the angles between columns of $A$ the same as angles between the columns of $R$ when $A=QR$ and $A^\top A=R^\top R$?

Published on 14 Apr 2026 - 0:52

score 54 · Answer 4 · 2026-04-15 21:05:27

54

Views

The property of symmetric matrices and Euclid inner product, about rank.

Published on 15 Apr 2026 - 21:05

score 77 · Answer 5 · 2026-04-15 12:36:33

77

Views

The property of symmetric matrix and its eigenvalue, in inner product space.

Published on 15 Apr 2026 - 12:36

score 627 · Answer 6 · 2026-04-13 12:59:10

627

Views

The proof of $\langle Ax,x\rangle=\langle x,Ax\rangle$ for all $x\in \mathbb C^n$ $\Rightarrow$ $A$ is Hermitian.

Published on 13 Apr 2026 - 12:59

score 221 · Answer 7 · 2026-04-14 14:52:13

221

Views

Lebesgue measure on finite dimensional inner product space

Published on 14 Apr 2026 - 14:52

score 46 · Answer 8 · 2026-04-12 23:31:27

If $T$ is a unitary linear operator in the complex space $(V, ⟨\cdot|\cdot⟩)$ is it also unitary in any other inner product space $(V, \cdot)$?

score 50 · Answer 9 · 2026-04-15 09:56:51

50

Views

Must an inverse of an inner product preserving operator be inner product preserving in an infinite dimensional space?

Published on 15 Apr 2026 - 9:56

score 71 · Answer 10 · 2026-04-13 18:03:25

71

Views

Orthogonal functions on the circle with constraints

Published on 13 Apr 2026 - 18:03

score 177 · Answer 11 · 2026-04-13 11:02:13

177

Views

How do we prove by contradiction that, if $\langle x,y\rangle = \langle x,z\rangle$ for all $x$, then $y=z$?

Published on 13 Apr 2026 - 11:02

score 678 · Answer 12 · 2026-04-12 06:44:33

678

Views

Weighted inner product of functions

Published on 12 Apr 2026 - 6:44

score 93 · Answer 13 · 2026-04-11 12:54:51

93

Views

Is the minimum angle between a cone and a vector achieved on an extreme ray?

Published on 11 Apr 2026 - 12:54

score 80 · Answer 14 · 2026-05-04 10:01:06

80

Views

How to solve vector equation $\textbf{x}+2(\textbf{x}^T\cdot\textbf{a})\cdot\textbf{x}=\textbf{b}$

Published on 04 May 2026 - 10:01

score 61 · Answer 15 · 2026-04-13 08:04:15

61

Views

Inner product of a function with a dual function

Published on 13 Apr 2026 - 8:04

List Question

Does $Ax+Bx=\lambda x$ imply $\langle Ax ,x \rangle + \langle Bx, x \rangle=\langle\lambda x, x \rangle$?

An alternative proof of Mashke's theorem for a case $K=\mathbb C$ or $K$ is a subfield of $\mathbb C$

Why are the angles between columns of $A$ the same as angles between the columns of $R$ when $A=QR$ and $A^\top A=R^\top R$?

The property of symmetric matrices and Euclid inner product, about rank.

The property of symmetric matrix and its eigenvalue, in inner product space.

The proof of $\langle Ax,x\rangle=\langle x,Ax\rangle$ for all $x\in \mathbb C^n$ $\Rightarrow$ $A$ is Hermitian.

Lebesgue measure on finite dimensional inner product space

If $T$ is a unitary linear operator in the complex space $(V, ⟨\cdot|\cdot⟩)$ is it also unitary in any other inner product space $(V, \cdot)$?

Must an inverse of an inner product preserving operator be inner product preserving in an infinite dimensional space?

Orthogonal functions on the circle with constraints

How do we prove by contradiction that, if $\langle x,y\rangle = \langle x,z\rangle$ for all $x$, then $y=z$?

Weighted inner product of functions

Is the minimum angle between a cone and a vector achieved on an extreme ray?

How to solve vector equation $\textbf{x}+2(\textbf{x}^T\cdot\textbf{a})\cdot\textbf{x}=\textbf{b}$

Inner product of a function with a dual function

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