Additional linear algebra topics, Eigenvalues and eigenvectors, To compute the eigenvalues for a square matrix – HP 48g Graphing Calculator User Manual
Page 184
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To compute the row-reduced echelon form of a matrix:
1
.
2
,
14
Enter the matrix onto the stack. If you are attempting to solve a
system of linear equations, the matrix should be the augmented
matrix representation of the system (see discussion above).
Optional: Set flag —54 if you do not want “tiny” elements replaced
with zero during the computation: Press
MODES)
F L F i G 54
m S F . “Tiny” elements, which can be generated due to
roundoff errors during computation, are those elements that are less
than 1 x times the size of the largest element in their column.
Unless you set flag —54, the HP 48 replaces any “tiny” elements
with zero.
Press
f'MTH
) M H
T
R
F fi C T R
R R E F .
Additional Linear Algebra Topics
The HP 48 offers a selection of other linear algebra commands that
give you additional problem-solving power and flexibility.
Eigenvalues and Eigenvectors
A square (n x n) matrix A is said to have an eigenvalue X and a
corresponding eigenvector x if Ax = Ax.
Eigenvalues are the roots of the characteristic equation,
det(A — AI) = 0, which is a polynomial of degree n. Thus, A has n
eigenvalues, although they are not always distinct. Each eigenvalue
has a corresponding eigenvector.
The HP 48 allows you to compute either the eigenvalues only (a
faster computation) or both the eigenvalues and their corresponding
eigenvectors.
To
compute the
eigenvalues
for
a square matrix:
1. Enter the square (n x n) matrix onto the stack.
2. Press fivrfHl
eigenvalues.
Mfl'l R fNXT) E G V L to compute a vector of n
14-20 Matrices and Linear Aigebra