Question

Show that $(Tx,Ty)=0$ if $(x,y)=0$ implies that $T$ is a multiple of a unitary map

score 253 · Answer 1 · 2026-03-25 16:03:45

253

Views

Show that $(Tx,Ty)=0$ if $(x,y)=0$ implies that $T$ is a multiple of a unitary map

Published on 25 Mar 2026 - 16:03

score 115 · Answer 2 · 2026-03-26 09:48:03

115

Views

Complex inner product spaces: are $A^A$ and $AA^$ always unitarily equivalent?

Published on 26 Mar 2026 - 9:48

score 2.1k · Answer 3 · 2026-04-03 06:14:29

2.1k

Views

Dot product of two vectors squared identity

Published on 03 Apr 2026 - 6:14

score 200 · Answer 4 · 2026-03-25 19:03:52

200

Views

Finite-dimensional unitary spaces: are $A^A$ and $AA^$ are always unitarily equivalent?

Published on 25 Mar 2026 - 19:03

score 697 · Answer 5 · 2026-03-30 01:53:09

697

Views

Direct sum of a subspace and its orthogonal complement

Published on 30 Mar 2026 - 1:53

score 480 · Answer 6 · 2020-06-08 16:15:41

480

Views

Proving conjugate property of Frobenius inner product over the complex field

Published on 08 Jun 2020 - 16:15

score 477 · Answer 7 · 2026-03-27 14:39:43

477

Views

Prove that T-cI is normal

Published on 27 Mar 2026 - 14:39

score 182 · Answer 8 · 2026-03-30 01:52:05

182

Views

Let $(V,\langle,\rangle)$ be a finite dimensional vector space. Let $T$ be a linear operator on V. Show that $\operatorname{Im}T=(\ker T^*)^\perp$

Published on 30 Mar 2026 - 1:52

score 608 · Answer 9 · 2020-06-09 11:25:13

608

Views

Prove that $||A||_2 = \max_{||x||_2=1, ||y||_2 = 1} |y^TAx|$

Published on 09 Jun 2020 - 11:25

score 52 · Answer 10 · 2020-06-10 03:47:44

The identity $||a||^2||b||^2||c||^2 + 2\langle a,b \rangle \langle b,c \rangle \langle c,a\rangle = \sum\limits_{cyc} ||a||^2 \langle b,c\rangle^2$

score 42 · Answer 11 · 2026-04-06 08:08:36

42

Views

Decomposition of the space of two-forms

Published on 06 Apr 2026 - 8:08

score 59 · Answer 12 · 2026-03-30 03:55:15

59

Views

How complex numbers can be compared in Cauchy-Schwarz inequality in an inner product space over the complex field

Published on 30 Mar 2026 - 3:55

score 234 · Answer 13 · 2026-03-25 19:05:05

234

Views

Infinite-dimensional inner product spaces: if $A^k = I$ for self-adjoint $A$ and for integer $k > 0$, then $A^2 = I$

Published on 25 Mar 2026 - 19:05

score 225 · Answer 14 · 2020-06-11 07:23:03

225

Views

Infinite-dimensional inner product spaces: if $A^3 = A^2$ for a normal operator $A$, then $A^2 = A$

Published on 11 Jun 2020 - 7:23

score 76 · Answer 15 · 2020-06-11 16:24:57

76

Views

What can we say if the inner products of two vectors ($u$ and $v$) with another vector ($x$) are equal? ($x$ is an eigenvector)

Published on 11 Jun 2020 - 16:24

List Question

Show that $(Tx,Ty)=0$ if $(x,y)=0$ implies that $T$ is a multiple of a unitary map

Complex inner product spaces: are $A^A$ and $AA^$ always unitarily equivalent?

Dot product of two vectors squared identity

Finite-dimensional unitary spaces: are $A^A$ and $AA^$ are always unitarily equivalent?

Direct sum of a subspace and its orthogonal complement

Proving conjugate property of Frobenius inner product over the complex field

Prove that T-cI is normal

Let $(V,\langle,\rangle)$ be a finite dimensional vector space. Let $T$ be a linear operator on V. Show that $\operatorname{Im}T=(\ker T^*)^\perp$

Prove that $||A||_2 = \max_{||x||_2=1, ||y||_2 = 1} |y^TAx|$

The identity $||a||^2||b||^2||c||^2 + 2\langle a,b \rangle \langle b,c \rangle \langle c,a\rangle = \sum\limits_{cyc} ||a||^2 \langle b,c\rangle^2$

Decomposition of the space of two-forms

How complex numbers can be compared in Cauchy-Schwarz inequality in an inner product space over the complex field

Infinite-dimensional inner product spaces: if $A^k = I$ for self-adjoint $A$ and for integer $k > 0$, then $A^2 = I$

Infinite-dimensional inner product spaces: if $A^3 = A^2$ for a normal operator $A$, then $A^2 = A$

What can we say if the inner products of two vectors ($u$ and $v$) with another vector ($x$) are equal? ($x$ is an eigenvector)

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