List questions from inner-products

Published on 11 Nov 2016 - 23:30

205

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Show $\alpha$ is selfadjoint.

Published on 27 Mar 2026 - 22:59

78

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To find the adjoint of $Τ_P$, where $Τ_P$ is the linear operator on $V$ defined by $Τ_P (A) = Ρ^{-1}ΑΡ$.

Published on 27 Mar 2026 - 22:57

45

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If $В$ is an arbitrary member of the inner product space, show that $L_b$ is unitarily equivalent to $R_{B^t}$.

Published on 31 Mar 2026 - 4:56

105

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Prove that if $\{v_1,v_2,\dots,v_n\}$ is orthonormal, then for any $v$, $\lVert v\rVert^2 \ge \Sigma_{j=1}^n \lvert \langle v,v_j \rangle \rvert$

Published on 13 Nov 2016 - 23:19

4.5k

Views

Showing that the dot product of a zero vector with any vector is 0.

Published on 14 Nov 2016 - 0:20

1.2k

Views

Orthogonal projection with respect to hermitian product

Published on 31 Mar 2026 - 3:31

435

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Determine an inner product space.

Published on 15 Nov 2016 - 8:36

122

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Complex conjugation in inner product space?

Published on 15 Nov 2016 - 9:26

678

Views

Ratio between inner products on a vector space

Published on 18 Nov 2016 - 12:14

40

Views

Image of closed unit ball and its closure contained in $\prod_{y \in \ell^\infty}[-\|y\|_\infty,\|y\|_\infty]$?

Published on 18 Nov 2016 - 23:05

1k

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Inner products equal implies the arguments are equal

Published on 19 Nov 2016 - 2:28

403

Views

Norm and inner product

Published on 08 Apr 2026 - 3:03

11k

Views

Eigenvalues and eigenvectors of a unitary operator

Published on 19 Nov 2016 - 15:13

94

Views

Simplifying inner product of the A-norm terms(part of proof)

Published on 19 Nov 2016 - 20:32

List Question

Visualizing inequality in arbitrary dimension

Show $\alpha$ is selfadjoint.

To find the adjoint of $Τ_P$, where $Τ_P$ is the linear operator on $V$ defined by $Τ_P (A) = Ρ^{-1}ΑΡ$.

If $В$ is an arbitrary member of the inner product space, show that $L_b$ is unitarily equivalent to $R_{B^t}$.

Prove that if $\{v_1,v_2,\dots,v_n\}$ is orthonormal, then for any $v$, $\lVert v\rVert^2 \ge \Sigma_{j=1}^n \lvert \langle v,v_j \rangle \rvert$

Showing that the dot product of a zero vector with any vector is 0.

Orthogonal projection with respect to hermitian product

Determine an inner product space.

Complex conjugation in inner product space?

Ratio between inner products on a vector space

Image of closed unit ball and its closure contained in $\prod_{y \in \ell^\infty}[-\|y\|_\infty,\|y\|_\infty]$?

Inner products equal implies the arguments are equal

Norm and inner product

Eigenvalues and eigenvectors of a unitary operator

Simplifying inner product of the A-norm terms(part of proof)

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