Function Jordan - HP 50g User Manual

Graphing calculator.

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,
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
x
= 0, x
1
2

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)
= 0.29, x
1
1
= 3.16, x
2
2
= 7.54, x
3
1
x
= 0, and x
1
3
= [ 1.00,0.79,–0.91]
= [1.00,-0.51, 0.65]
= [-0.03, 1.00, 0.84]
x
= 0.
2
3
T
,
T
,
T
.
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