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eig

  

compute the eigenvalues of a MapleMatrix or MatlabMatrix in MATLAB(R)

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

eig(X)

eig(X, Y)

eig(X, Y, eigenvectors=true, balanced=true)

Parameters

X

-

MapleMatrix, or MatlabMatrix

Y

-

(optional) MapleMatrix or a MatlabMatrix

eigenvectors=[true|false]

-

(optional) return eigenvectors

balanced=[true|false]

-

(optional) balance the matrix

Description

• 

The eig command computes the eigenvalues of a matrix using MATLAB®.

• 

If you specify the option 'eigenvectors'='true', then both the eigenvectors and the eigenvalues of the matrix are returned. The default is 'eigenvectors'='false'. In this form, the eigenvectors are the columns of the first matrix returned, and the eigenvalues are the entries along the diagonal of the second matrix returned.

• 

If you specify the option 'balanced'='false', then a preliminary balancing step is not computed first. The balancing step  improves the conditioning of the matrix X. The default is 'balanced'='true'.

• 

The call Matlab[eig](X, Y) solves the "generalized eigenvalue problem"; that is, it finds the roots of the polynomial detlambdaYX.

• 

By default a Vector of eigenvalues is returned. When you specify 'eigenvectors'='true', an additional Matrix of eigenvectors is also returned.

Examples

Define the Maple matrix

withMatlab:

maplematrix_aMatrix1,2,3,3,4,5,6,7,8

maplematrix_a:=123345678

(1)

The Eigenvalues of this MapleMatrix are computed as

Matlab[eig]maplematrix_a

[    14.0663729752107667    ]

[                           ]

[   -1.06637297521077667    ]

[                           ]

[                        -15]

[-0.379901471867316940 10   ]

To get the eigenvectors also

vects,valsMatlab[eig]maplematrix_a,'eigenvectors'='true':

vects

[-0.265647760732583504 ,  -0.744428627863832570 , 0.408248290463863628]

[                                                                     ]

[-0.491207120532433317 , -0.190701223873281478 , -0.816496580927726145]

[                                                                     ]

[-0.829546160232207730 ,  0.639889882112543052 ,  0.408248290463862573]

vals

[14.0663729752107667 ,     0. ,     0.]

[                                     ]

[0. ,     -1.06637297521077667 ,    0.]

[                                     ]

[                                  -15]

[0. , 0. , -0.379901471867316940 10   ]

See Also

LinearAlgebra[Eigenvalues]

LinearAlgebra[Eigenvectors]

Matlab

Matlab[det]

Matlab[evalM]

Matlab[inv]

MatlabMatrix

 


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