List questions from adjoint-operators

Published on 12 Nov 2016 - 22:23

77

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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 13 Nov 2016 - 11:09

54

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Form of adjoint matrix.

Published on 13 Nov 2016 - 15:42

28

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Let $V,W$ be complex inner product spaces. Fix $v \in V$ and $w \in W$ and define $T(u)=\langle u,v\rangle_V w$. Find $T^:W \rightarrow V$

Published on 14 Nov 2016 - 2:21

246

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Orthogonal to a range

Published on 15 Nov 2016 - 3:52

937

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Adjoint matrix as pseudo-inverse

Published on 26 Mar 2026 - 14:17

327

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Matrix of self-adjoint operator such that every element of the diagonal is $0$.

Published on 20 Nov 2016 - 22:08

140

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Show that $\text{ker}(T^*T)=\text{ker}(T)$

Published on 04 Dec 2016 - 15:55

64

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How can we describe $\ker (T)$ and $\ker( T^*)$ in this case?

Published on 26 Mar 2026 - 7:58

237

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Prove $T^2 = (T^*)T$ if $T$ is positive-definite

Published on 11 Dec 2016 - 0:30

83

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Showing $(A^T A)^2 = A^T A$ , where matrix A has orthornomal rows

Published on 27 Dec 2016 - 22:41

560

Views

Self-adjoint bounded operators in a Hilbert space

Published on 29 Dec 2016 - 13:22

50

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Working on linear maps

Published on 29 Dec 2016 - 15:31

175

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How is the "adjoint representation" related to generic group representations?

Published on 29 Dec 2016 - 16:22

93

Views

Finding the adjoint of $\alpha: p(X)\to(X+1)p(X)$

Published on 29 Dec 2016 - 22:45

List Question

Show $\alpha$ is selfadjoint.

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

Form of adjoint matrix.

Let $V,W$ be complex inner product spaces. Fix $v \in V$ and $w \in W$ and define $T(u)=\langle u,v\rangle_V w$. Find $T^:W \rightarrow V$

Orthogonal to a range

Adjoint matrix as pseudo-inverse

Matrix of self-adjoint operator such that every element of the diagonal is $0$.

Show that $\text{ker}(T^*T)=\text{ker}(T)$

How can we describe $\ker (T)$ and $\ker( T^*)$ in this case?

Prove $T^2 = (T^*)T$ if $T$ is positive-definite

Showing $(A^T A)^2 = A^T A$ , where matrix A has orthornomal rows

Self-adjoint bounded operators in a Hilbert space

Working on linear maps

How is the "adjoint representation" related to generic group representations?

Finding the adjoint of $\alpha: p(X)\to(X+1)p(X)$

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