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Change mode to Approx and repeat the entry, to get the following
eigenvalues:
[(1.38,2.22), (1.38,-2.22), (-1.76,0)]
.
Function EGV
Function EGV (EiGenValues and eigenvectors) produces the eigenvalues and
eigenvectors of a square matrix. The eigenvectors are returned as the
columns of a matrix, while the corresponding eigenvalues are the components
of a vector.
For example, in ALG mode, the eigenvectors and eigenvalues of the matrix
listed below are found by applying function EGV:
The result shows the eigenvalues as the columns of the matrix in the result list.
To see the eigenvalues we can use: GET(ANS(1),2), i.e., get the second
element in the list in the previous result. The eigenvalues are:
In summary,
λ
1
= 0.29,
x
1
= [ 1.00,0.79,–0.91]
T
,
λ
2
= 3.16,
x
2
= [1.00,-0.51, 0.65]
T
,
λ
3
= 7.54,
x
1
= [-0.03, 1.00, 0.84]
T
.
Note
: A symmetric matrix produces all real eigenvalues, and its eigenvectors
are mutually perpendicular. For the example just worked out, you can check
that
x
1
•
x
2
= 0,
x
1
•
x
3
= 0, and
x
2
•
x
3
= 0.
