Question

If $(S_{n}x,y)\to(Sx,y)$ and $(T_{n}x,y)\to(Tx,y)$ for all $x,y\in H$, then $(S_{n}T_{n}x,y)\to(STx,y)$ for all $x,y\in H$.

score 26 · Answer 1 · 2020-04-16 15:04:38

26

Views

If $(S_{n}x,y)\to(Sx,y)$ and $(T_{n}x,y)\to(Tx,y)$ for all $x,y\in H$, then $(S_{n}T_{n}x,y)\to(STx,y)$ for all $x,y\in H$.

Published on 16 Apr 2020 - 15:04

score 519 · Answer 2 · 2020-04-16 20:43:04

519

Views

Do there exist inner product spaces for families of real valued functions other than weighted integrals?

Published on 16 Apr 2020 - 20:43

score 112 · Answer 3 · 2020-04-16 23:38:41

112

Views

Determine $R(T)$ and $N(T)$

Published on 16 Apr 2020 - 23:38

score 357 · Answer 4 · 2020-04-16 23:43:30

357

Views

Prove $N(T^T) = N(T)$, and $\dim(R(T^T))=\dim(R(T))$.

Published on 16 Apr 2020 - 23:43

score 508 · Answer 5 · 2020-04-17 14:46:29

508

Views

What is the second order derivative of the dot product $\mathbf{u}(\mathbf{x})\cdot\mathbf{v}(\mathbf{x})$ with respect to $\mathbf{x}$?

Published on 17 Apr 2020 - 14:46

score 594 · Answer 6 · 2026-03-25 17:53:09

594

Views

All $n$ dimensional real inner product spaces are isomorphic to $\mathbb{R}^n$

Published on 25 Mar 2026 - 17:53

score 37 · Answer 7 · 2020-04-18 12:02:34

37

Views

An integral, can I prove that it is an inner product, and if so for what space?

Published on 18 Apr 2020 - 12:02

score 285 · Answer 8 · 2026-03-25 19:01:54

285

Views

Field homomorphism is onto

Published on 25 Mar 2026 - 19:01

score 508 · Answer 9 · 2020-04-18 14:37:23

508

Views

Prove that the dot product of two timelike vectors cannot be $0$

Published on 18 Apr 2020 - 14:37

score 118 · Answer 10 · 2026-03-25 22:09:53

118

Views

Bounds for Matrix Inner Product based on singular values

Published on 25 Mar 2026 - 22:09

score 126 · Answer 11 · 2020-04-20 07:52:43

126

Views

Matrix of a linear transformation on basis

Published on 20 Apr 2020 - 7:52

score 103 · Answer 12 · 2026-03-26 09:09:57

103

Views

A basis with $e_i\cdot e_j<0$ implies a dual basis with $f_i\cdot f_j>0$?

Published on 26 Mar 2026 - 9:09

score 206 · Answer 13 · 2026-03-26 08:00:40

206

Views

If $u_i\cdot u_j<0$ for all $u_0,...,u_n\in\Bbb R^n$, then the $u_i$ cannot lie in the same halfspace?

Published on 26 Mar 2026 - 8:00

score 855 · Answer 14 · 2026-03-25 17:45:37

855

Views

Proof to show that a matrix $A$ is Hermitian

Published on 25 Mar 2026 - 17:45

score 59 · Answer 15 · 2026-03-26 09:10:38

59

Views

On the monotonicity of angles between dual basis vectors

Published on 26 Mar 2026 - 9:10

List Question

If $(S_{n}x,y)\to(Sx,y)$ and $(T_{n}x,y)\to(Tx,y)$ for all $x,y\in H$, then $(S_{n}T_{n}x,y)\to(STx,y)$ for all $x,y\in H$.

Do there exist inner product spaces for families of real valued functions other than weighted integrals?

Determine $R(T)$ and $N(T)$

Prove $N(T^T) = N(T)$, and $\dim(R(T^T))=\dim(R(T))$.

What is the second order derivative of the dot product $\mathbf{u}(\mathbf{x})\cdot\mathbf{v}(\mathbf{x})$ with respect to $\mathbf{x}$?

All $n$ dimensional real inner product spaces are isomorphic to $\mathbb{R}^n$

An integral, can I prove that it is an inner product, and if so for what space?

Field homomorphism is onto

Prove that the dot product of two timelike vectors cannot be $0$

Bounds for Matrix Inner Product based on singular values

Matrix of a linear transformation on basis

A basis with $e_i\cdot e_j<0$ implies a dual basis with $f_i\cdot f_j>0$?

If $u_i\cdot u_j<0$ for all $u_0,...,u_n\in\Bbb R^n$, then the $u_i$ cannot lie in the same halfspace?

Proof to show that a matrix $A$ is Hermitian

On the monotonicity of angles between dual basis vectors

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