Question

Show that $\left \langle A^tx, y \right \rangle = \left \langle x, Ay \right \rangle$

score 318 · Answer 1 · 2020-07-25 17:34:47

318

Views

Show that $\left \langle A^tx, y \right \rangle = \left \langle x, Ay \right \rangle$

Published on 25 Jul 2020 - 17:34

score 267 · Answer 2 · 2020-07-25 22:01:05

267

Views

Sufficient Condition to be Hilbert Space: Convergence of series of orthonormal vectors with $\ell^2$ coefficients implies completeness?

Published on 25 Jul 2020 - 22:01

score 156 · Answer 3 · 2020-07-26 23:24:06

156

Views

Asking for a hint: Convex sets and inner product spaces

Published on 26 Jul 2020 - 23:24

score 37 · Answer 4 · 2026-03-26 22:53:18

37

Views

Find a positive-definite matrix $B$ such that $\langle A,B\rangle_F=0$

Published on 26 Mar 2026 - 22:53

score 110 · Answer 5 · 2020-07-30 18:31:17

110

Views

Show that in a Hilbert space, $||x+\alpha y|| \ge ||x|| \,\forall\,\alpha\in\mathbb{C}\implies (x,y)=0$

Published on 30 Jul 2020 - 18:31

score 192 · Answer 6 · 2016-07-05 23:08:05

192

Views

Projections satisfying $\| Px-Qx \| <\|x \|$ for nonzero $x$?

Published on 05 Jul 2016 - 23:08

score 380 · Answer 7 · 2016-07-06 11:37:30

380

Views

Calculating adjoint operator for standard inner product of matrices

Published on 06 Jul 2016 - 11:37

score 122 · Answer 8 · 2026-04-05 20:54:13

122

Views

How is defined the inner product $g_p$ on $T_p \mathbb{R}^n/\Gamma$ at the point $p$?

Published on 05 Apr 2026 - 20:54

score 1.7k · Answer 9 · 2016-07-06 22:30:48

1.7k

Views

Matrix representing inner product?

Published on 06 Jul 2016 - 22:30

score 119 · Answer 10 · 2026-03-27 19:31:45

119

Views

Seemingly strange exercise on unitary Hermitian operator

Published on 27 Mar 2026 - 19:31

score 767 · Answer 11 · 2026-03-28 21:27:09

767

Views

Show quadratic form is positive definite

Published on 28 Mar 2026 - 21:27

score 81 · Answer 12 · 2026-03-30 07:08:56

81

Views

Find $\inf _{a,b,c\in \mathbb C}\int _{[-\pi,\pi]}|x+a+b\cos x+c\sin x | ^2dx$

Published on 30 Mar 2026 - 7:08

score 354 · Answer 13 · 2026-03-26 19:00:45

354

Views

Does the Parseval identity imply the completeness of an orthonormal system?

Published on 26 Mar 2026 - 19:00

score 194 · Answer 14 · 2026-03-30 07:07:23

194

Views

Prove the completion of the span of $ \left\{ e^{i\lambda t} \right\} _{\lambda\in \mathbb R}$ is not separable

Published on 30 Mar 2026 - 7:07

score 34 · Answer 15 · 2016-07-10 21:11:29

34

Views

Dimension and separability of $\ell^2(I)$?

Published on 10 Jul 2016 - 21:11

List Question

Show that $\left \langle A^tx, y \right \rangle = \left \langle x, Ay \right \rangle$

Sufficient Condition to be Hilbert Space: Convergence of series of orthonormal vectors with $\ell^2$ coefficients implies completeness?

Asking for a hint: Convex sets and inner product spaces

Find a positive-definite matrix $B$ such that $\langle A,B\rangle_F=0$

Show that in a Hilbert space, $||x+\alpha y|| \ge ||x|| \,\forall\,\alpha\in\mathbb{C}\implies (x,y)=0$

Projections satisfying $\| Px-Qx \| <\|x \|$ for nonzero $x$?

Calculating adjoint operator for standard inner product of matrices

How is defined the inner product $g_p$ on $T_p \mathbb{R}^n/\Gamma$ at the point $p$?

Matrix representing inner product?

Seemingly strange exercise on unitary Hermitian operator

Show quadratic form is positive definite

Find $\inf _{a,b,c\in \mathbb C}\int _{[-\pi,\pi]}|x+a+b\cos x+c\sin x | ^2dx$

Does the Parseval identity imply the completeness of an orthonormal system?

Prove the completion of the span of $ \left\{ e^{i\lambda t} \right\} _{\lambda\in \mathbb R}$ is not separable

Dimension and separability of $\ell^2(I)$?

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