- 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...
-
matrix A
satisfying the
equation A*A = AA* is
diagonalizable. (The
converse does not hold
because diagonalizable matrices may have non-orthogonal eigenspaces...
-
converse is also true; that is, if two
diagonalizable matrices commute, they are
simultaneously diagonalizable. But if you take any two
matrices that...
- 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...
-
linearly independent eigenvectors. Not all
matrices are
diagonalizable;
matrices that are not
diagonalizable are
called defective matrices.
Consider the following...
- 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...
-
eigenvectors of A form a
basis if and only if A is
diagonalizable. A
matrix that is not
diagonalizable is said to be defective. For
defective matrices,...
- are said to be
diagonalizable. More generally, an
endomorphism and a
matrix are also said
diagonalizable, if they
become diagonalizable after extending...
