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eig

  

compute the eigenvalues and eigenvectors of a matrix

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

l = eig(A)

[V,L] = eig(A)

[V,L,N] = eig(A)

Parameters

A

-

matrix

Description

• 

The function eig(A) computes the eigenvalues and eigenvectors of the matrix A. That is, for each eigenvalue lambda of A, it solves the linear system (I * lambda - A) * X= 0  for X.

• 

When the function is called using the form l := eig(A), the returned value of l is a column Vector containing the eigenvalues of A.

• 

When the function is called using the form V,L := eig(A), the returned value of L is a Matrix with the eigenvalues of A along the main diagonal, and the returned value of V is a Matrix whose columns are the eigenvectors of A.

• 

When the function is called using the form V,L,N := eig(A), L and V are as described above. N is a row vector of indices, one for each linearly independent eigenvector of A, such that the vector corresponding to the ith column of V has eigenvalue L[N[i],N[i]].

Examples

withMTM:

AMatrix1,2,1,2,4,2,2,8,1

A:=121242281

(1)

leigA

l:=03+22322

(2)

V,LeigA

V,L:=93+225+7222+22932257222223216+225+7221622572214111,3+220003220000

(3)

V,L,NeigA

V,L,N:=3293+225+7222+22932257222221416+225+72216225722111,00003+22000322,123

(4)

See Also

LinearAlgebra[Eigenvalues]

LinearAlgebra[Eigenvectors]

MTM[jordan]

MTM[poly]

MTM[svd]

 


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