Question

Orthogonality in terms of two inner products in $W_0^{1,2}(U)$

score 34 · Answer 1 · 2026-04-10 05:17:13

34

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Orthogonality in terms of two inner products in $W_0^{1,2}(U)$

Published on 10 Apr 2026 - 5:17

score 42 · Answer 2 · 2026-04-15 15:15:22

42

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Prove that $\|v\|$ is the supremum of this set.

Published on 15 Apr 2026 - 15:15

score 499 · Answer 3 · 2026-04-13 20:45:32

499

Views

How to prove that the dot product is distributive (non-coplanar vectors)?

Published on 13 Apr 2026 - 20:45

score 180 · Answer 4 · 2026-04-14 07:48:46

180

Views

Find a matrix which is orthogonal to two given matrix w.r.t the given inner product $\langle S,T\rangle = \text{Tr}(ST)$

Published on 14 Apr 2026 - 7:48

score 474 · Answer 5 · 2026-04-13 08:31:35

474

Views

When does the norm of the sum of $n$ vectors equal the sum of the norms of the vectors?

Published on 13 Apr 2026 - 8:31

score 951 · Answer 6 · 2026-04-14 04:50:05

951

Views

Proving the dot product cosine identity for dimensions $> 2$

Published on 14 Apr 2026 - 4:50

score 136 · Answer 7 · 2026-04-14 02:27:04

136

Views

Prove that $\det R = \pm 1$ iff $R \in \mathrm{Isom}(V)$, without using $\det R = \det R^T$

Published on 14 Apr 2026 - 2:27

score 44 · Answer 8 · 2026-04-13 00:22:43

44

Views

Theoretical Machine Learning: How to calculate the expected risk of a model with unknown distribution $\hat{h}$?

Published on 13 Apr 2026 - 0:22

score 630 · Answer 9 · 2026-04-12 13:05:47

630

Views

Unitary operators, inner products and unit operators with Dirac notation

Published on 12 Apr 2026 - 13:05

score 86 · Answer 10 · 2026-04-14 18:40:09

Which of the following determines an inner product over the space of real continuous functions with continuous first derivatives?

score 27 · Answer 11 · 2026-04-14 03:58:04

27

Views

Prove the set $A := \{\bar{x} \in V | \langle\bar{x}, \bar{v}\rangle \geq c \}$ is connected in $(V, d)$

Published on 14 Apr 2026 - 3:58

score 45 · Answer 12 · 2026-04-16 16:43:24

45

Views

How to determine coefficients of the polynomial about $\alpha$ which represent $w \in \mathbb{Q}[\alpha]$?

Published on 16 Apr 2026 - 16:43

score 535 · Answer 13 · 2026-04-16 14:28:23

535

Views

Image and kernel related to inner product

Published on 16 Apr 2026 - 14:28

score 40 · Answer 14 · 2026-04-17 14:24:48

40

Views

Mistake in derivation of preservation inner product when multiplied by orthogonal matrix.

Published on 17 Apr 2026 - 14:24

score 351 · Answer 15 · 2026-04-12 13:11:13

351

Views

Dot product in tensor algebra

Published on 12 Apr 2026 - 13:11

List Question

Orthogonality in terms of two inner products in $W_0^{1,2}(U)$

Prove that $\|v\|$ is the supremum of this set.

How to prove that the dot product is distributive (non-coplanar vectors)?

Find a matrix which is orthogonal to two given matrix w.r.t the given inner product $\langle S,T\rangle = \text{Tr}(ST)$

When does the norm of the sum of $n$ vectors equal the sum of the norms of the vectors?

Proving the dot product cosine identity for dimensions $> 2$

Prove that $\det R = \pm 1$ iff $R \in \mathrm{Isom}(V)$, without using $\det R = \det R^T$

Theoretical Machine Learning: How to calculate the expected risk of a model with unknown distribution $\hat{h}$?

Unitary operators, inner products and unit operators with Dirac notation

Which of the following determines an inner product over the space of real continuous functions with continuous first derivatives?

Prove the set $A := \{\bar{x} \in V | \langle\bar{x}, \bar{v}\rangle \geq c \}$ is connected in $(V, d)$

How to determine coefficients of the polynomial about $\alpha$ which represent $w \in \mathbb{Q}[\alpha]$?

Image and kernel related to inner product

Mistake in derivation of preservation inner product when multiplied by orthogonal matrix.

Dot product in tensor algebra

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