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 …

So unitary Hermitian matrices are precisely the matrices admitting a complete set of orthonormal eigenvectors such that the corresponding eigenvalues are $\pm 1$.

Mar 23, 2015 · SUMMARY The discussion focuses on the representation of a general 2x2 unitary matrix in the form of U = (e i α 1 cos θ e i α 2 sin θ e i α 3 sin θ e i α 4 cos θ). Key conditions …

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 …

Apr 23, 2021 · Find a unitary matrix given eigenvectors and eigenvalues Ask Question Asked 4 years, 8 months ago Modified 4 years, 8 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} …

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, …

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 …

Orthogonal matrix and unitary matrix Ask Question Asked 13 years, 1 month ago Modified 12 years, 1 month ago

So by composing the two transformations (diagonalization, then taking the diagonal matrix to the required form), I'll get a unitary transformation taking the real antisymmetric matrix to another …