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- What is the difference between isometric and unitary operators on a . . .
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 nonunitary operator and a unitary operator)
- linear algebra - Whats 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
- linear algebra - How do i prove that this matrix is unitary . . .
How do i prove that this matrix is unitary? Ask Question Asked 1 year, 10 months ago Modified 1 year, 10 months ago
- linear algebra - 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} \mathbf {U}^* \end {equation} Definition (Vector $2$ -norm)
- linear algebra - Singular value decomposition for unitary matrices . . .
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
- prove that an operator is unitary - Mathematics Stack Exchange
prove that an operator is unitary Ask Question Asked 5 years, 5 months ago Modified 5 years, 5 months ago
- If H is Hermitian, show that $e^ {iH}$ is unitary
In the case where H is acting on a finite dimensional vector space, you can essentially view it as a matrix, in which case (by for example the BCH formula) the relation you state in a) is valid More generally if $ [A,B]=0$ then the product of exponentials is just the exponential of the sum There may be subtleties in the more general case, but I doubt you'd even be interested in those As for
- Definition Unitary Group - Mathematics Stack Exchange
@TobiasKildetoft The unitary group (and finite groups fields in general) come up quite often in geometric settings, as the finite classical groups act naturally on projective geometries preserving quadrics polar spaces (in fact the article mentioned by the poster is on geometry)
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