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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
.
Function JORDAN
Function JORDAN is intended to produce the diagonalization or Jordan-cycle
decomposition of a matrix. In RPN mode, given a square matrix A, function
JORDAN produces four outputs, namely:
• The minimum polynomial of matrix A (stack level 4)
• The characteristic polynomial of matrix A (stack level 3)
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.