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)
Square root of unitary matrix - Mathematics Stack Exchange 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 - Norm preservation properties of a unitary matrix . . . 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 - How do i prove that this matrix 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 - 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
diagonalize block matrices with special type of unitary matrices 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
Definition of unitary operators - Mathematics Stack Exchange So for a unitary operator apart from the condition which you wrote we also have it for its adjoint, that is, $$ \left<U^*x, U^*y\right> = \left<x, y\right> $$ Example of a map which is an isometry, but not unitary: