**Eigenvalues of 3 x 3 Matrices**

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

The programs for the Casio Prizm and TI-84+ gives eigenvalues of 3 x 3 matrices.

For the HP 39gii has the functions EIGENVAL for eigenvalues.

Example:

A = [[2, -2, 3][-1, 0, 1][6, -3, 3]]

Eigenvalues:

≈ 0.2465, -1.8447, 6.5982

Casio Prizm:

EIGEN3

Eigenvalues of a 3 × 3 Matrix

Circa 2011 - 244 bytes

a+bi

"3 × 3 Matrix"? → Mat A

Mat A[1,1] + Mat A[2,2] + Mat A[3,3] → T

(Mat A)² → Mat B

Mat B[1,1] + Mat B[2,2] + Mat B[3,3] → U

Solve(-X^3 + X^2 × T + X × 1/2 × (U-T^2) + Det Mat A,0)→ R ◢

-R^2 + R × T - T^2 ÷ 2 + U ÷ 2 → A

-R + T → B

1/2 × (B - √(4A + B^2)) → E ◢

1/2 × (B + √(4A + B^2)) → F ◢

"STORED IN R, E, F"

TI-84+:

EIGEN3

Eigenvalues of a 3 × 3 matrix - 193 bytes

12/3/12

a+bi

Input "3 X 3 MATRIX:", [A]

[A](1,1) + [A](2,2) + [A](3,3) → T

[A]² → [B]

[B](1,1) + [B](2,2) + [B](3,3) → U

solve(-X³ + X² T + .5X(U-T²) + det([A]), X, 0) → R

Pause R

-R² + RT - T²/2 + U/2 → A

-R + T → B

.5(B - √(4A+B²)) → E

.5(B + √(4A+B²)) → F

Pause E

Pause F

This blog is property of Edward Shore. 2012

To finish my trip through the world of non alpha numeric code I tried to make a non alpha numeric Python or non alpha numeric Batch script but I wasn't able to do so. Numerology

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