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 …
General form for 2 x 2 unitary matrices - Physics Forums
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 …
linear algebra - Matrices which are both unitary and Hermitian ...
are both unitary and Hermitian (for 0 ≤ θ ≤ 2π 0 ≤ θ ≤ 2 π). I call the latter type trivial, since its columns equal to plus/minus columns of the identity matrix. Do such matrices have any …
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
Show that the eigenvalues of a unitary matrix have modulus $1$
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, …
Norm preservation properties of a unitary matrix
Norm preservation properties of a unitary matrix Ask Question Asked 9 years, 1 month ago Modified 10 months ago
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 …
What is the general expression for a unitary $3 \times 3$ matrix?
Jun 19, 2017 · 2 I have not checked this paper myself, but an answer is probably contained in the rather recent paper: Gil, J. J. (2018). Parametrization of 3× 3 unitary matrices based on …
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 …