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 nonunitary …

Apr 23, 2021 · Now, this matrix has eigenvalues 1 and − 1, and eigenvectors (1, 0) and (0, 1), as desired. It just remains to check that indeed A is unitary. For example, you can argue that this is the …

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 space then …

Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 6 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} \mathbf {U}^*. \end …

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 value …

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 geometries …

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 $B$.

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. More …

Nov 7, 2016 · The result does not give me the diagonal matrix with the desired eigenvalues though. Also, Google search did not yield a single nicely explained way to do a unitary transform of a normal …