-
corresponding to the same eigenvalue,
together with the zero vector, is
called an
eigenspace, or the
characteristic space of T ****ociated with that eigenvalue. If...
- finite-dimensional
vector space has an
eigenvalue λ,
corresponding to some
eigenspace Vλ. Let Vλ⊥ be its
orthogonal complement. It is
clear that, with respect...
-
called the
eigenspace of λ,
while the
vector space ker((A − λI)n)
consists of all
generalized eigenvectors, and is
called the
generalized eigenspace. The geometric...
- {\displaystyle A} need not be diagonalizable. The
dimension of the
generalized eigenspace corresponding to a
given eigenvalue λ {\displaystyle \lambda } is the...
-
generalization of the
notion of an eigenvalue, and the
corresponding eigenspace is
called a
weight space.
Given a set S of n × n {\displaystyle n\times...
-
belong to an
eigenspace will
retain their direction. A
vector that is the sum of two or more non-zero
vectors belonging to
different eigenspaces will be tilted...
- is a
generalized eigenvector, and so each
eigenspace is
contained in the ****ociated
generalized eigenspace. This
provides an easy
proof that the geometric...
- Consequently, the
eigenspace ****ociated to r is one-dimensional. (The same is true for the left
eigenspace, i.e., the
eigenspace for AT, the transpose...
- In mathematics, a
rigged Hilbert space (Gelfand triple,
nested Hilbert space,
equipped Hilbert space) is a
construction designed to link the distribution...
- A is
diagonalizable if and only if the sum of the
dimensions of the
eigenspaces is n. Or, equivalently, if and only if A has n
linearly independent eigenvectors...
