Wednesday, December 5, 2012

Numeric CAS Part 10 - Eigenvalues of 2 x 2 Matrices

Eigenvalues of 2 x 2 Matrices

Many graphing calculators that do not have CAS (computer algebraic systems) do not have eigenvalues and eigenvector functions.

The program for the Casio Prizm gives eigenvalues. The TI-84+ program gives both eigenvalues and eigenvectors.

For the HP 39gii has the functions EIGENVAL and EIGENVV for eigenvalues and eigenvectors, respectively.

Example:
A = [[2, 7][-3, 9]]

Eigenvalues: ≈ 5.5 ± 2.9580i


Casio Prizm:

Eigenvalues of a 2 × 2 Matrix
EIGEN2 - 136 Bytes

a+bi
"2 × 2 MATRIX:"? → Mat A
Mat A[1,1] + Mat A[2,2] → T
Det Mat A→ D
(T+√(T^2-4D))÷2 → R ◢
(T-√(T^2-4D))÷2 → S ◢
"λS STORED IN R,S"


TI-84+:

EIGEN2
Eigenvalues of 2 × 2 matrices - Approximately 280 bytes
Bonus! A pair of eigenvectors are given
5/15/2011

a+bi
Input "2 X 2 MATRIX:", [J]
[J](1,1) + [J](2,2) → T
det([J]) → D
(T + √(T^2 - 4D))/2 → U
(T - √(T^2 - 4D))/2 → V
Disp "EIGENVAL. U"
Pause U
(U - [J](1,1)) / [J](1,2) → A
√(1 + A^2)⁻¹ * [[1][A]] → [H]
Disp "EIGENVEC. [H]"
Pause [H]
(V - [J](1,1)) / [J](1,2) → B
√(1 + B^2)⁻¹ * [[1][B]] → [I]
Disp "EIGENVAL. V"
Pause V
Disp "EIGENVECT. [I]"
Pause [I]




This blog is property of Edward Shore. 2012

1 comment:

  1. Hi Edward, i followed your guide in programming my TI-84+ to calculate the eigenvects & vals but upon executing the program, it always reflect ERR:UNDEFINED. any idea what might be the cause of problem? Any help is greatly appreciated!!

    ReplyDelete

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