Operators and Hilbert Space
Michael A. Parker · 2009
Every linear operator can be represented as a matrix once having identified a basis set for the vector space. Although the operator and matrix appear to be different, the two mappings produce the same result once the results are suitably interpreted. Stated in other words, there exists an isomorphism between the space of linear operators and matrices that ensures that the two vector spaces have identical properties. Therefore, the theorems in the present chapter can be stated and proved using either the matrix or operator formalism.