# Function Egv - HP 49g+ User Manual

Graphing calculator.

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