The operator this particular transformation is a scalar multiplication. The operator is sometimes referred to as what the linear transformation exactly entails.

No, the expected value is not a linear operator, because it isn't an operator (a map from a vector space to itself) at all. The expected value is a linear form, i.e. a linear map from a vector space …

Mar 28, 2016 · That is, applying the linear operator to each basis vector in turn, then writing the result as a linear combination of the basis vectors gives us the columns of the matrices as …

Feb 18, 2019 · The zero operator is a linear operator, i.e. a linear map from a vector space to a vector space (possibly the same one). It has the property that it maps any member of the first …

Dec 4, 2016 · What exactly you don't understand? You know what a linear operator is, right? If yo do, then check the given $\;T\;$ is a linear operator, and if you don't then read it elsewhere as …

May 19, 2017 · A matrix representation for a linear map describes how the transformation acts in the coordinate space (what you think as an implicit isomorphism is simply the definition).

Easiest way to prove that an operator is linear? Ask Question Asked 13 years, 5 months ago Modified 13 years, 5 months ago

Feb 27, 2016 · That a linear operator is bounded means simply that it is Lipschitz. It turns out to be equivalent to continuity in case of normed spaces.

Jan 16, 2016 · Explore related questions linear-algebra reference-request category-theory hilbert-spaces adjoint-functors See similar questions with these tags.

Aug 22, 2024 · How to extend a bounded densely defined linear operator? Ask Question Asked 10 years, 11 months ago Modified 1 year, 1 month ago