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 …

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 …

Dec 6, 2020 · Show that if $A$ and $B$ are unitary matrices, then $C = A \\otimes B$ is unitary.

Apr 23, 2021 · Find a unitary matrix given eigenvectors and eigenvalues Ask Question Asked 4 years, 11 months ago Modified 4 years, 11 months ago

Jul 20, 2012 · On certain decomposition of unitary symmetric matrices Ask Question Asked 13 years, 8 months ago Modified 12 years, 3 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 value …

Apr 13, 2015 · You wrote that similarity does not preserve symmetry (or rather conjugate symmetry in case of complex matrices) but preserves positive definiteness. What does this mean in particular …

Mar 31, 2020 · This allows one to form "stable" homotopy groups $\pi_k^s (U)$ of the unitary groups. (Note: "Stable" has a different meaning in comparison to "stable" homotopy groups of the spheres.)

The Gram-Schmidt procedure gives you an orthonormal basis, which when arragned into a matrix gives a unitary matrix. I included the normalization step in the procedure, so the determinant of the …

May 20, 2020 · (r) $$ in the domain is, in fact, a unitary operator. My answer relies on two definitions: the definition of a bounded operator and the definition of a unitary operator. These definitions are given …