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#### Search: #### Eigenvalues

Function: eigenvalues (<M>) 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.

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### Related Examples

##### eigenvalues-matrix

A:matrix([1,0,0],[0,1...

eigenvalues(A);

Calculate

##### eigenvalues-expand-matrix-numer

expand((x-1)^2+(y-1)^...

A:matrix([1,2],[2,1]);

eigenvalues(A), numer;

Calculate

##### eigenvalues-hessian

eigenvalues(hessian((...

Calculate

##### eigenvalues-matrix

a:matrix([3-p,0],[2,3...

eigenvalues(a);

Calculate

##### eigenvalues-ev-matrix-ratsimp-solve-sqrt

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

B:ev(A,a=-1);

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

Calculate

##### eigenvalues-matrix

A: matrix([2,7],[3,9]);

eigenvalues(A);

Calculate

##### eigenvalues-matrix

A : matrix([a, b], [b...

EigVal:eigenvalues(A);

Calculate

##### eigenvalues-invert-jacobian-matrix

A: jacobian ([a*If*Sh...

B: jacobian ([gh*Ih, ...

C: invert (B);

Calculate

K:matrix([-2*k,k,0.0]...

eigenvalues(K);

Calculate

##### eigenvalues-matrix

m:matrix([-2,1],[1,2]);

eigenvalues(m);

Calculate 