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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 - 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 - How do i prove that this matrix is unitary . . .
How do i prove that this matrix is unitary? Ask Question Asked 1 year, 11 months ago Modified 1 year, 11 months ago
- How to prove that a matrix $U$ is unitary, if and only if the columns . . .
By definition a matrix $T$ is unitary if $T^*T=I $ For two real matrices $A,B$, the $i,j$ entry of $AB$ is the inner product of the $i$ row of $A$ and $j$ column of $B$
- linear algebra - Let $A$ be a normal matrix. Prove that if $|\lambda . . .
Let A A be a normal matrix Prove that if |λ| = 1 | λ | = 1 for all eigenvalues λ λ of A A then A A is unitary Ask Question Asked 5 years, 6 months ago Modified 5 years, 6 months ago
- 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
- Definition of unitary operators - Mathematics Stack Exchange
In infinite-dimensional spaces, unitary operators are bijective with the inverse being equal to their adjoint For a finite-dimensional vector space X X and every linear operator V X X V X X, injectivity (of V V) is equivalent to its surjectivity
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