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 · Find a unitary matrix given eigenvectors and eigenvalues Ask Question Asked 5 years ago Modified 4 years, 11 months ago

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 …

I just can't show that a unitary matrix $U$ is unitarily diagonizable. I know I need to show that $U$ is unitarily similar to a diagonal matrix, and this result is presumably a consequence of the spectral …

Jun 21, 2020 · prove that an operator is unitary Ask Question Asked 5 years, 10 months ago Modified 5 years, 9 months ago

Nov 7, 2021 · is there any unitary matrix that has determinant that is not $\pm 1$ or $\pm i$? Ask Question Asked 4 years, 5 months ago Modified 4 years, 5 months ago

Aug 29, 2024 · Some related posts I found on the site are: Definition of Unitary Operators: Why do we need surjectivity or boundedness? definition of unitary operator Unitary Operator bounded?

Jun 19, 2017 · What is the general expression for a unitary $3 \times 3$ matrix? Ask Question Asked 8 years, 10 months ago Modified 2 years, 3 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 …

Very good proof! However, an interesting thing is that you can perhaps stop at the third last step, because an equivalent condition of a unitary matrix is that its eigenvector lies on the unit circle, so …