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Additional
Defective matrix
English Wikipedia - The Free Encyclopedia
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Defective matrix
In
linear algebra
, a
defective matrix
is a
square matrix
that does not have a complete
basis
of
eigenvectors
, and is therefore not
diagonalizable
. In particular, an
n
×
n
matrix is defective if and only if it does not have
n
linearly independent
eigenvectors. A complete basis is formed by augmenting the eigenvectors with
generalized eigenvectors
, which are necessary for solving defective systems of
ordinary differential equations
and other problems.
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