A compact normal operator ( in particular, a normal operator on a finite-dimensional linear space ) is unitarily diagonalizable.
22.
A compact normal operator ( in particular, a normal operator on a finite-dimensional linear space ) is unitarily diagonalizable.
23.
This implies the usual spectral theorem : every normal operator on a finite-dimensional space is diagonalizable by a unitary operator.
24.
The concept of normal matrices can be extended to normal operators on infinite dimensional Hilbert spaces and to normal elements in C *-algebras.
25.
Eigenvectors of a normal operator corresponding to different eigenvalues are orthogonal, and a normal operator stabilizes the orthogonal complement of each of its eigenspaces.
26.
Eigenvectors of a normal operator corresponding to different eigenvalues are orthogonal, and a normal operator stabilizes the orthogonal complement of each of its eigenspaces.
27.
The technical master may also be required to step in if the normal operator has encountered a problem, and does not know how to correct it.
28.
With stronger assumptions, when " T " is a normal operator acting on a Hilbert space, the domain of the functional calculus can be broadened.
29.
A normal operator has a representation A = B + i C where B, C are self-adjoint and commute, i . e . BC = CB.
30.
In the latter case, the Gelfand Naimark representation theorem is one avenue in the development of spectral theory for normal operators, and generalizes the notion of diagonalizing a normal matrix.
