Maxima Function
eigenvalues (M)
eivals(M)
Returns a list of two lists containing the eigenvalues of the matrix M. The first sublist of the return value is the list of eigenvalues of the matrix, and the second sublist is the list of the multiplicities of the eigenvalues in the corresponding order.
eivals
is a synonym for eigenvalues
.
eigenvalues
calls the function solve
to find the roots of the
characteristic polynomial of the matrix.
Sometimes solve
may not be able to find the roots of the polynomial;
in that case some other functions in this
package (except innerproduct
, unitvector
, columnvector
and
gramschmidt
) will not work.
In some cases the eigenvalues found by solve
may be complicated expressions.
(This may happen when solve
returns a not-so-obviously real expression
for an eigenvalue which is known to be real.)
It may be possible to simplify the eigenvalues using some other functions.
The package eigen.mac
is loaded automatically when
eigenvalues
or eigenvectors
is referenced.
If eigen.mac
is not already loaded,
load ("eigen")
loads it.
After loading, all functions and variables in the package are available.