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The Maxima on-line user's manual

Algebra Calculator

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Eigenvalues

Function: eigenvalues (<M>)

A: matrix([16165,-5444,-5444 ],[-5444,16165,-5444],[-5444,-5444,17815]);
eigenvalues(A);

Function: 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.

There are also some inexact matches for eigenvalues. Try ?? eigenvalues to see them.

(%o1)                                true
(%i2) 

Related Examples

eigenvalues-eigenvectors-invert-matrix

A:matrix([-19/6,11/3]...

eigenvectors(A);

eigenvalues(A);

Calculate

eigenvalues

eigenvalues([[1,1,2,3...

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eigenvalues

? eigenvalues;

Calculate

eigenvalues-eigenvectors-matrix

M:matrix([1,0],[0,1]);

eigenvalues(M);

eigenvectors(M);

Calculate

eigenvalues-matrix

a:matrix([2,3],[-1,1]);

eigenvalues(a);

Calculate

eigenvalues-ev-matrix-ratsimp-solve-sqrt

A:matrix([a, (sqrt(5)...

B:ev(A,a=0);

sol:ratsimp(solve(B[1...

Calculate

eigenvalues-eigenvectors-invert-matrix

f: matrix([0, b1 +p *...

v: matrix([d+v+r1, 0]...

i: invert(v);

Calculate

eigenvalues-matrix

M: matrix([1/2, -1/4]...

eigenvalues(M);

Calculate

eigenvalues-jacobian-subst

J:jacobian([(1-x)*(1*...

A:subst([x=1/2,y=1/2]...

eigenvalues(A);

Calculate

eigenvalues-invert-matrix

mat3:matrix([a,e,e,0,...

mat4:invert(mat3);

eigenvalues(mat4);

Calculate