- In
linear algebra, a
square matrix A {\displaystyle A} is
called diagonalizable or non-defective if it is
similar to a
diagonal matrix. That is, if there...
-
algebraic group is said to be
diagonalizable if it is
isomorphic to a
subgroup of Dn, the
group of
diagonal matrices. A
diagonalizable group defined over a field...
-
matrix is
represented in
terms of its
eigenvalues and eigenvectors. Only
diagonalizable matrices can be
factorized in this way. When the
matrix being factorized...
- 3D
manifold of
rotation matrices. A
method for
finding log A for a
diagonalizable matrix A is the following: Find the
matrix V of
eigenvectors of A (each...
-
matrix A
satisfying the
equation A*A = AA* is
diagonalizable. (The
converse does not hold
because diagonalizable matrices may have non-orthogonal eigenspaces...
- does not have a
complete basis of eigenvectors, and is
therefore not
diagonalizable. In particular, an n × n {\displaystyle n\times n}
matrix is defective...
- &e^{a_{n}}\end{bmatrix}}.} This
result also
allows one to
exponentiate diagonalizable matrices. If A = UDU−1 then eA = UeDU−1,
which is
especially easy to...
- \lambda _{1},\ldots ,\lambda _{n}} , then C ( p ) {\displaystyle C(p)} is
diagonalizable as C ( p ) = V − 1 D V {\displaystyle C(p)=V^{-1}\!DV} ,
where D is...
-
converse is also true; that is, if two
diagonalizable matrices commute, they are
simultaneously diagonalizable. But if you take any two
matrices that...
-
which itself has an eigenvector, and thus by
induction is
diagonalizable. Conversely,
diagonalizable operators are
easily seen to be semi-simple, as invariant...
