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Eigenvalues of a 4x4 matrix with Ti-84  (also complex)

Explanation of calculating the eigen values of a matrix on your Ti84

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With the Ti84 Basic program EIGENVAL.8XP the eigenvalues of a matrix can be calculated (also complex). Useful for control system theory. For a 3*3 and 4*4 matrix, it is time-consuming if programs like Matlab or Maple are not available. With the program EIGENVAL.8xp, the eigenvalues up to a 4*4 matrix can be calculated. Knowledge of the Application PlySmlt2 is required

2 examples are given: first, the eigenvalues of a 3*3 matrix is calculated. In the second examples, the eigen values of a 4*4 matrix are calculated.

Follow the next steps for calculating the eigenvalues (see the figures). It is advised to run the program Adefault.8xp first to get enough memory space.

1: make a 4*4 matrix [A] and fill the rows and the columns with the numbers. (Key 2nd Matrix-edit)

For a 3*3 or 2*2 matrix, still make a 4*4 matrix and fill the remaining places with 0.

2: Run the program EIGENVAL.8xp. The program calculates a4, a3, a2,a1,a0 of the equation: Solving det(A-λI)=0 results in :

     

Resulting equation

eigen value equation determined from the matrix

Example of a 3*3 Matrix:

Take a 4*4 matrix and fill the empty places with 0 in the 4*4 matrix for a 3* 3 problem 

Input for the matrix
Start of the eigenvalue program
coefficients ao,a1,a2,a3,a4 calculated with the program eigenvalue

a4, a3, a2, a1, a0 are saved in List L1 and are ready to use in the app PlySmlt2

Run the Application PlySmlt2 and choose Poly Root Finder, degree 4 and after NEXT choose Load 2nd L1 and Solve. The eigenvalues are calculated.  

Start of the Polynomial Root Finder toi calulate the eigen values
Eigenvalues calculated by Ti-84 plus

Eigenvalues

Comparison with Matlab shows that the program is correct. It is also tested on a 4x4 matrix

Matrix input for calulating  eigenvalues with Matlab
eigenvalues results by MatlabTi

For questions or a request for the program EIGENVAL.8XP, mail to ti84.org@gmail.com

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There is a 4X4 matrix example on : 

measured since 8-9-2022        Copyright © All rights reserved 

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