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eigenvectors

Maxima Function

Calling Sequence

eigenvectors (M)
eivects(M)

Description

takes a matrix M as its argument and returns a list of lists the first sublist of which is the output of eigenvalues and the other sublists of which are the eigenvectors of the matrix corresponding to those eigenvalues respectively. The calculated eigenvectors and the unit eigenvectors of the matrix are the right eigenvectors and the right unit eigenvectors respectively.

eivects is a synonym for eigenvectors.

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.

The flags that affect this function are:

nondiagonalizable is set to true or false depending on whether the matrix is nondiagonalizable or diagonalizable after eigenvectors returns.

hermitianmatrix when true, causes the degenerate eigenvectors of the Hermitian matrix to be orthogonalized using the Gram-Schmidt algorithm.

knowneigvals when true causes the eigen package to assume the eigenvalues of the matrix are known to the user and stored under the global name listeigvals. listeigvals should be set to a list similar to the output eigenvalues.

The function algsys is used here to solve for the eigenvectors. Sometimes if the eigenvalues are messy, algsys may not be able to find a solution. In some cases, it may be possible to simplify the eigenvalues by first finding them using eigenvalues command and then using other functions to reduce them to something simpler. Following simplification, eigenvectors can be called again with the knowneigvals flag set to true.

eigenvalues SciMax Toolbox eighth