linear algebra - What's the interpretation of a unitary matrix ...
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 …
linear algebra - Matrices which are both unitary and Hermitian ...
So unitary Hermitian matrices are precisely the matrices admitting a complete set of orthonormal eigenvectors such that the corresponding eigenvalues are $\pm 1$.
A unitary matrix taking a real matrix to another real matrix, is it an ...
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 …
Given a unitary matrix $U$, how do I find $A$ such that $U=e
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 …
Find a unitary matrix given eigenvectors and eigenvalues
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
Norm preservation properties of a unitary matrix
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} …
Hermitian matrix versus unitary matrix - Mathematics Stack …
May 21, 2020 · From Wikipedia: In linear algebra, a complex square matrix U U is unitary if its conjugate transpose U∗ U ∗ is also its inverse, that is, if U∗U = UU∗ = I, U ∗ U = U U ∗ = I,, …
How to do a unitary diagonalization of a normal matrix?
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 …
linear algebra - Why do the columns of a unitary matrix form an ...
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...
Is the Transpose Conjugate of a Unitary Matrix Equal to the …
Dec 22, 2014 · Hi, A unitary matrix should have it transpose conjugate equal to its inverse. Please confirm that this statement is correct and check attached matrix as...