Question

Prove that for the defined $\langle .,. \rangle$ there exist $0 < a \le b$ such that $a\|x\| \le \|x\|_\ast ≤ b\|x\|$ for all $x \in H$.

score 39 · Answer 1 · 2026-03-27 07:17:11

39

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Prove that for the defined $\langle .,. \rangle$ there exist $0 < a \le b$ such that $a\|x\| \le \|x\|_\ast ≤ b\|x\|$ for all $x \in H$.

Published on 27 Mar 2026 - 7:17

score 404 · Answer 2 · 2026-02-23 04:57:44

404

Views

To show that the space of all transversal lagrangian subspaces is contractible

Published on 23 Feb 2026 - 4:57

score 2.1k · Answer 3 · 2026-04-05 22:35:45

2.1k

Views

Geometric definition of the dot product in $n$-dimensional vector spaces

Published on 05 Apr 2026 - 22:35

score 235 · Answer 4 · 2020-03-26 21:31:21

235

Views

Properties of norm induced by positive definite matrix

Published on 26 Mar 2020 - 21:31

score 103 · Answer 5 · 2026-03-27 05:36:05

103

Views

Exchanging dot product with matrix multiplication

Published on 27 Mar 2026 - 5:36

score 111 · Answer 6 · 2026-03-29 16:49:18

111

Views

Determine two polynomials that are orthogonal to a inner product

Published on 29 Mar 2026 - 16:49

score 440 · Answer 7 · 2020-03-29 08:19:42

440

Views

Prove or disprove $closure$ of $span S$= Perp of S perp

Published on 29 Mar 2020 - 8:19

score 649 · Answer 8 · 2026-03-27 14:51:57

649

Views

$n$th order Taylor polynomial formula varies with the inner product?

Published on 27 Mar 2026 - 14:51

score 52 · Answer 9 · 2026-03-26 07:57:03

52

Views

Scalar Product on $\mathbb{R}^3$

Published on 26 Mar 2026 - 7:57

score 67 · Answer 10 · 2026-03-30 01:29:59

67

Views

Square root of an intrinsic rotation in 2D inner product space

Published on 30 Mar 2026 - 1:29

score 54 · Answer 11 · 2020-04-01 08:00:26

54

Views

Conjugate symmetry in normed spaces

Published on 01 Apr 2020 - 8:00

score 215 · Answer 12 · 2026-03-27 06:07:51

215

Views

Proving $(e_{j})(k)=\frac{1}{\sqrt{N}}e^{(2\pi ijk)/N}$ is an orthonormal basis for $\mathbb C^n$

Published on 27 Mar 2026 - 6:07

score 1.5k · Answer 13 · 2020-04-01 14:44:00

1.5k

Views

Squared norm of sum of vectors

Published on 01 Apr 2020 - 14:44

score 823 · Answer 14 · 2026-03-25 17:52:53

823

Views

Inner product gives vector space isomorphism with dual space

Published on 25 Mar 2026 - 17:52

score 128 · Answer 15 · 2020-04-01 23:11:42

128

Views

Prove $\sum_{i=1}^{n}v_i^t \cdot v_i = I$ for orthonormal base

Published on 01 Apr 2020 - 23:11

List Question

Prove that for the defined $\langle .,. \rangle$ there exist $0 < a \le b$ such that $a\|x\| \le \|x\|_\ast ≤ b\|x\|$ for all $x \in H$.

To show that the space of all transversal lagrangian subspaces is contractible

Geometric definition of the dot product in $n$-dimensional vector spaces

Properties of norm induced by positive definite matrix

Exchanging dot product with matrix multiplication

Determine two polynomials that are orthogonal to a inner product

Prove or disprove $closure$ of $span S$= Perp of S perp

$n$th order Taylor polynomial formula varies with the inner product?

Scalar Product on $\mathbb{R}^3$

Square root of an intrinsic rotation in 2D inner product space

Conjugate symmetry in normed spaces

Proving $(e_{j})(k)=\frac{1}{\sqrt{N}}e^{(2\pi ijk)/N}$ is an orthonormal basis for $\mathbb C^n$

Squared norm of sum of vectors

Inner product gives vector space isomorphism with dual space

Prove $\sum_{i=1}^{n}v_i^t \cdot v_i = I$ for orthonormal base

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