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 …

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 …

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 1, 2015 · I believe the way you propose is quite standard. For a more general understanding of exponentiation, maybe look for an introductory course on Lie groups and Lie algebras, but for simple …

In infinite-dimensional spaces, unitary operators are bijective with the inverse being equal to their adjoint. For a finite-dimensional vector space X X and every linear operator V X X V X X, injectivity …

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 $B$.

Jun 7, 2020 · Let A A be a normal matrix. Prove that if |λ| = 1 | λ | = 1 for all eigenvalues λ λ of A A then A A is unitary. Ask Question Asked 5 years, 6 months ago Modified 5 years, 6 months ago

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

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

May 11, 2015 · A unitary operator is a diagonalizable operator whose eigenvalues all have unit norm. If we switch into the eigenvector basis of U, we get a matrix like: \begin {bmatrix}e^ {ia}&0&0\\0&e^ …