linear-algebra functional-analysis
Definition
Spectral Representation
A spectral representation is a way of describing a linear operator or matrix by decomposing it into parts associated with its eigenvalues and eigenvectors.
In finite dimensions, this often means writing the operator in a basis in which it becomes diagonal, or as a sum of projections onto eigenspaces.
Intuition
A spectral representation breaks an operator into the parts that act independently on each spectral component.