spectral theorem

Normal operators are important because the spectral theorem holds for them.

These basic facts play an important role in the proof of the spectral theorem below.

The spectral theorem can be extended to normal operators in general.

The spectral theorem extends to a more general class of matrices.

This can be seen as a consequence of the spectral theorem for normal operators.

Again, by the spectral theorem, such a matrix takes the general form:

However, the main ideas can be understood using the finite-dimensional spectral theorem.

However, when A is normal, an affirmative answer is given by the spectral theorem.

The spectral theorem implies that the rank is independent of the Jordan frame.

The square root is the positive semidefinite one given by the spectral theorem.

The above spectral theorem holds for real or complex Hilbert spaces.

The spectral theorem can again be used to obtain a standard equation akin to the one given above.

A precise version of the spectral theorem in this case is:

In general, spectral theorem for self-adjoint operators may take several equivalent forms.

Numerous well-known results may be derived from the Freudenthal spectral theorem.

This is the crux of proof for spectral theorem in the matricial case.

However, as noted above, the spectral theorem also holds for normal operators on a Hilbert space.

There is also a spectral theorem for self-adjoint operators that applies in these cases.

This is the spectral theorem for normal operators.

The academic activities of the School were inaugurated with a two-day national workshop on the spectral theorem.

There is also a version of the spectral theorem that applies to unbounded normal operators.

Normal operators are characterized by the spectral theorem.

The spectral theorem still holds for unbounded normal operators, but usually requires a different proof.

The spectral theorem shows that all normal operators admit invariant subspaces.

Spectral theorem in the form of multiplication operator.