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 …

Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 7 months ago Modified 5 years, 7 months ago

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

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 …

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 …

Jan 20, 2014 · From all this, we see that U U and V V are unique up to unitary transformations of the eigenspaces of M∗M M ∗ M and unitary transformations of (image M)⊥ (image M) ⊥.

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 …

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 …

Apr 22, 2025 · Unitary conjugation between self-adjoint operators up to commuting remainder Ask Question Asked 9 months ago Modified 9 months ago

So I'm trying to understand why the columns of a unitary matrix form an orthonormal basis. I know it has something to do with the inner product, but I don't fully understand that either (we learned all of this …