Category:Definitions/Linear Transformations on Hilbert Spaces

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This category contains definitions related to Linear Transformations on Hilbert Spaces.
Related results can be found in Category:Linear Transformations on Hilbert Spaces.

Let $V, W$ be vector spaces over a field (or, more generally, division ring) $K$.

A mapping $A: V \to W$ is a linear transformation if and only if:

$\forall v_1, v_2 \in V, \lambda \in K: \map A {\lambda v_1 + v_2} = \lambda \map A {v_1} + \map A {v_2}$

That is, a homomorphism from one vector space to another.