A stronger notion is unitary equivalence, i.e., similarity induced by a unitary transformation (since these are the isometric isomorphisms of Hilbert space), which again cannot happen between a …

Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 5 months ago Modified 5 years, 5 months ago

Definition (Unitary matrix). A unitary matrix is a square matrix $\mathbf {U} \in \mathbb {K}^ {n \times n}$ such that \begin {equation} \mathbf {U}^* \mathbf {U} = \mathbf {I} = \mathbf {U} …

Unitary matrices are the complex versions, and they are the matrix representations of linear maps on complex vector spaces that preserve "complex distances". If you have a complex vector …

Jan 5, 2024 · How do i prove that this matrix is unitary? Ask Question Asked 1 year, 11 months ago Modified 1 year, 11 months ago

Jan 13, 2021 · I know the title is strange, but there are many instances in quantum information in which one is interested not in diagonalizing a unitary matrix, but instead in finding its singular …

In the case where H is acting on a finite dimensional vector space, you can essentially view it as a matrix, in which case (by for example the BCH formula) the relation you state in a) is valid. …

Dec 8, 2017 · @TobiasKildetoft The unitary group (and finite groups/fields in general) come up quite often in geometric settings, as the finite classical groups act naturally on projective …

Mar 22, 2016 · Prove that the DFT Matrix is Unitary Ask Question Asked 9 years, 8 months ago Modified 1 year, 1 month ago

By definition a matrix $T$ is unitary if $T^*T=I.$ For two real matrices $A,B$, the $i,j$ entry of $AB$ is the inner product of the $i$ row of $A$ and $j$ column of $B$.