What is the difference between isometric and unitary operators on …
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 isometry and a unitary operator (or between any …
Proving the Product of Unitary Matrices is also Unitary
2016年10月5日 · Unitary equivalence of sums of unitary equivalent hermitian matrices. 0. Convex combination of unitary ...
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 space then instead of using the scaler product like you would in a real vector space, you use the Hermitian product .
abstract algebra - prove that an operator is unitary - Mathematics ...
2020年6月21日 · $\begingroup$ Both of the facts you include in the edit are easy to prove. For the first one, it is just a matter of writing it down.
Prove that $e^{iAt}$ is unitary if $A$ is Hermitian
2021年3月13日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
operator theory - If H is Hermitian, show that $e^{iH}$ is unitary ...
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
linear algebra - Singular value decomposition for unitary matrices ...
2021年1月13日 · I know the title is strange, but there are many instances in quantum information in which one is interested not in diagonalizing a unitary matrix, but instead in finding its singular value decompos...
linear algebra - Norm preservation properties of a unitary matrix ...
Let $\mathbb{K} \in \{\mathbb{R},\mathbb{C}\}$ be either the field of real numbers $\mathbb{R}$ or the field of complex numbers $\mathbb{C}$.
Decomposition of a unitary matrix - Mathematics Stack Exchange
2013年11月7日 · Is anyone aware of a decomposition of a unitary matrix into a product of a special unitary matrix and the rest? Edit: A unitary matrix is a matrix that satisfies $\mathbf{U}\mathbf{U}^\dagger=1$ where $1$ is the unit matrix. Now assume I have a matrix $\mathbf{U}$ with this property. Is there a known decomposition
On certain decomposition of unitary symmetric matrices
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