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

1 All of the previous answers attempt to prove/justify why the expected value is linear. But the question asks whether the expected value is a linear operator. And the answer is: No, the …

When is the image of a linear operator closed? Ask Question Asked 14 years, 9 months ago Modified 1 year, 7 months ago

The book says an operator is linear if you get a constant * the operator back: $L [f (x)]=cf (x)$. I cannot integrate $f (s)ds$ without knowing what $f (s)$ is.

May 3, 2012 · Easiest way to prove that an operator is linear? Ask Question Asked 13 years, 7 months ago Modified 13 years, 7 months ago

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 …

Jun 15, 2017 · Transpose and adjoint of a linear operator Ask Question Asked 8 years, 5 months ago Modified 2 years, 1 month ago

The irreversibility of this step indicates that, while the square root function is operator monotone in our case, the square function is not. (Thanks for julien for pointing out that.)

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 …

Aug 22, 2024 · How to extend a bounded densely defined linear operator? Ask Question Asked 11 years, 1 month ago Modified 1 year, 3 months ago