Question

prove that $\lambda$ is eigenvalue of $T$ if and only if $\bar{\lambda}$ is eigenvalue for $T^*$

score 2.3k · Answer 1 · 2026-03-25 22:09:13

2.3k

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prove that $\lambda$ is eigenvalue of $T$ if and only if $\bar{\lambda}$ is eigenvalue for $T^*$

Published on 25 Mar 2026 - 22:09

score 237 · Answer 2 · 2026-03-27 19:29:15

237

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Where did the "Outer" and "Inner" Product nomenclature come from?

Published on 27 Mar 2026 - 19:29

score 45 · Answer 3 · 2018-05-04 01:18:15

45

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Pythagorean Law for Inner Product Spaces

Published on 04 May 2018 - 1:18

score 60 · Answer 4 · 2026-03-25 15:56:46

60

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Notation with Complex inner product space question

Published on 25 Mar 2026 - 15:56

score 2.3k · Answer 5 · 2018-05-06 06:54:21

2.3k

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How do you prove that (A,B) = trace(AB) is an inner product?

Published on 06 May 2018 - 6:54

score 112 · Answer 6 · 2026-03-25 04:42:22

112

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Finding the basis that results from an inner space

Published on 25 Mar 2026 - 4:42

score 1.3k · Answer 7 · 2026-03-25 06:08:56

1.3k

Views

Finding angle between 2 vectors using inner product

Published on 25 Mar 2026 - 6:08

score 422 · Answer 8 · 2018-05-06 15:50:20

422

Views

Prove $\langle u,v \rangle = uAv^* $ defines an inner product.

Published on 06 May 2018 - 15:50

score 813 · Answer 9 · 2018-05-07 19:45:49

813

Views

Basis in respect of an inner product

Published on 07 May 2018 - 19:45

score 106 · Answer 10 · 2026-03-28 08:42:38

106

Views

Verify Pythagorean Law for Normed Linear Space / Inner Product Space

Published on 28 Mar 2026 - 8:42

score 48 · Answer 11 · 2018-05-08 14:38:36

48

Views

Inner Product - Gramm-Schmidt Process

Published on 08 May 2018 - 14:38

score 1.2k · Answer 12 · 2026-03-25 23:10:05

1.2k

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Examples which show $\|\cdot\|_p$ on $L^p$ is not induced by an inner product (Parallelogram law)

Published on 25 Mar 2026 - 23:10

score 37 · Answer 13 · 2026-03-26 15:16:41

37

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Distance between a point and a plan

Published on 26 Mar 2026 - 15:16

score 306 · Answer 14 · 2026-03-24 22:01:17

306

Views

Any connections between Cauchy–Schwarz inequality and continuity/boundedness?

Published on 24 Mar 2026 - 22:01

score 221 · Answer 15 · 2026-03-26 22:32:04

221

Views

Prove inner-product inequality $\Bigl (\sum_{i=1}^k \langle u\;,\;e_i \rangle \langle v\;,\;e_i \rangle \Bigr)^2≤ \Vert u \Vert^2 \, \Vert v \Vert^2$

Published on 26 Mar 2026 - 22:32

List Question

prove that $\lambda$ is eigenvalue of $T$ if and only if $\bar{\lambda}$ is eigenvalue for $T^*$

Where did the "Outer" and "Inner" Product nomenclature come from?

Pythagorean Law for Inner Product Spaces

Notation with Complex inner product space question

How do you prove that (A,B) = trace(AB) is an inner product?

Finding the basis that results from an inner space

Finding angle between 2 vectors using inner product

Prove $\langle u,v \rangle = uAv^* $ defines an inner product.

Basis in respect of an inner product

Verify Pythagorean Law for Normed Linear Space / Inner Product Space

Inner Product - Gramm-Schmidt Process

Examples which show $\|\cdot\|_p$ on $L^p$ is not induced by an inner product (Parallelogram law)

Distance between a point and a plan

Any connections between Cauchy–Schwarz inequality and continuity/boundedness?

Prove inner-product inequality $\Bigl (\sum_{i=1}^k \langle u\;,\;e_i \rangle \langle v\;,\;e_i \rangle \Bigr)^2≤ \Vert u \Vert^2 \, \Vert v \Vert^2$

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