List questions from adjoint-operators | MathQa

An identity regarding linear operators and their adjoint between Hilbert spaces

Published on 12 Jan 2025 - 8:27

Why is $\sqrt{T^*T}$ self-adjoint?

Published on 12 Jan 2025 - 18:20

Characteristic polynomial of adjoint

Published on 12 Jan 2025 - 8:26

Why do we need an orthonormal basis to represent the adjoint of the operator?

Published on 12 Jan 2025 - 8:27

Is it true you use adjoint for linear transforms while you use transpose for matrix representation of linear transforms?

Published on 12 Jan 2025 - 8:26

Adjoint representation - A working example

Published on 12 Jan 2025 - 8:27

$T$ is surjective if and only if the adjoint $T^*$ is an isomorphism (onto its image)

Published on 12 Jan 2025 - 8:27

Determining adjoint operator between spaces with different inner products

Published on 12 Jan 2025 - 8:27

Suppose that $T$ is a normal operator on $V$. Show that $\|T(v+w)\|=10$.

Published on 12 Jan 2025 - 8:27

Operator $T^*$ surjective iff $T$ topologically injective

Published on 12 Jan 2025 - 8:27