Question

Prove that $\left \{ v_1,v_2,...,v_n\right \}$ is an orthogonal basis of $V$.

score 95 · Answer 1 · 2026-04-15 02:43:29

95

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Prove that $\left \{ v_1,v_2,...,v_n\right \}$ is an orthogonal basis of $V$.

Published on 15 Apr 2026 - 2:43

score 39 · Answer 2 · 2026-04-13 13:45:16

39

Views

convergence of a sequence of inner products

Published on 13 Apr 2026 - 13:45

score 23 · Answer 3 · 2026-04-16 22:37:17

23

Views

Positive-definiteness propertys doubts of a inner product ($[x,x]=0\,\,\Leftrightarrow\,\, x=0\,\,\,$ & $\,\,\,x\neq 0\,\,\Rightarrow\,\, [x,x]>0$).

Published on 16 Apr 2026 - 22:37

score 85 · Answer 4 · 2026-03-26 17:46:08

85

Views

Existence and uniqueness of the adjoint of a linear map.

Published on 26 Mar 2026 - 17:46

score 110 · Answer 5 · 2026-04-11 16:37:37

110

Views

Method explanation for proof used in the following proposition: If $(Sz,z)=(Tz,z)\forall z \in X$, then $S=T$.

Published on 11 Apr 2026 - 16:37

score 762 · Answer 6 · 2026-04-16 06:58:51

762

Views

A subspace whose orthogonal complement is {0}

Published on 16 Apr 2026 - 6:58

score 142 · Answer 7 · 2026-04-11 08:44:02

142

Views

Finding the orthogonal complement of a subset of a Hilbert space

Published on 11 Apr 2026 - 8:44

score 147 · Answer 8 · 2026-04-08 18:59:56

147

Views

Does dot product not change with transformation

Published on 08 Apr 2026 - 18:59

score 177 · Answer 9 · 2026-04-13 21:35:22

177

Views

Is the construction of gradient for this infinite dimensional Hilbert space well-defined?

Published on 13 Apr 2026 - 21:35

score 65 · Answer 10 · 2026-04-12 13:32:28

65

Views

Scalar and cross product: perpendicularity and parallelism

Published on 12 Apr 2026 - 13:32

score 54 · Answer 11 · 2026-04-15 21:42:27

54

Views

Show that $\{ x \in X: \langle w, x\rangle = b \}$ has dimension one less than $X$

Published on 15 Apr 2026 - 21:42

score 717 · Answer 12 · 2026-04-12 01:07:04

717

Views

Lagrange's identity: scalar and cross product

Published on 12 Apr 2026 - 1:07

score 309 · Answer 13 · 2026-04-10 23:38:19

309

Views

Understanding a proof that "the columns of a unitary matrix are orthonormal"

Published on 10 Apr 2026 - 23:38

score 23 · Answer 14 · 2026-04-17 05:36:46

23

Views

Show that there exists $d=(1-t)a+tc$ with $t\in(0,1)$ such that $||b-a||=||b-d||$

Published on 17 Apr 2026 - 5:36

score 230 · Answer 15 · 2026-04-19 03:49:06

230

Views

Calculating gradient for inner product of variable matrix

Published on 19 Apr 2026 - 3:49

List Question

Prove that $\left \{ v_1,v_2,...,v_n\right \}$ is an orthogonal basis of $V$.

convergence of a sequence of inner products

Positive-definiteness propertys doubts of a inner product ($[x,x]=0\,\,\Leftrightarrow\,\, x=0\,\,\,$ & $\,\,\,x\neq 0\,\,\Rightarrow\,\, [x,x]>0$).

Existence and uniqueness of the adjoint of a linear map.

Method explanation for proof used in the following proposition: If $(Sz,z)=(Tz,z)\forall z \in X$, then $S=T$.

A subspace whose orthogonal complement is {0}

Finding the orthogonal complement of a subset of a Hilbert space

Does dot product not change with transformation

Is the construction of gradient for this infinite dimensional Hilbert space well-defined?

Scalar and cross product: perpendicularity and parallelism

Show that $\{ x \in X: \langle w, x\rangle = b \}$ has dimension one less than $X$

Lagrange's identity: scalar and cross product

Understanding a proof that "the columns of a unitary matrix are orthonormal"

Show that there exists $d=(1-t)a+tc$ with $t\in(0,1)$ such that $||b-a||=||b-d||$

Calculating gradient for inner product of variable matrix

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