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.
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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 :
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Resulting equation
![eigen value equation determined from the matrix](https://static.wixstatic.com/media/5887e2_0985dd4cb6a6497b84714ff8e62c94c0~mv2.jpg/v1/fill/w_995,h_46,al_c,lg_1,q_80,usm_2.00_1.00_0.00,enc_avif,quality_auto/Knipsel_JPG.jpg)
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](https://static.wixstatic.com/media/5887e2_de04848731724513a3e5c5719d46ee52~mv2.jpg/v1/fill/w_947,h_244,al_c,q_80,usm_2.00_1.00_0.00,enc_avif,quality_auto/fig123_JPG.jpg)
![Start of the eigenvalue program](https://static.wixstatic.com/media/5887e2_d8ddb81ae1944c499be54b2b204f49f5~mv2.jpg/v1/fill/w_947,h_238,al_c,lg_1,q_80,usm_2.00_1.00_0.00,enc_avif,quality_auto/wix2l_JPG.jpg)
![coefficients ao,a1,a2,a3,a4 calculated with the program eigenvalue](https://static.wixstatic.com/media/5887e2_32fc9af28bfd4e298b0f5b9951694386~mv2.jpg/v1/fill/w_141,h_37,al_c,q_80,usm_0.66_1.00_0.01,blur_2,enc_avif,quality_auto/wix3l_JPG.jpg)
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](https://static.wixstatic.com/media/5887e2_311df79d97774b21ab188e03dc4e5959~mv2.jpg/v1/fill/w_143,h_37,al_c,q_80,usm_0.66_1.00_0.01,blur_2,enc_avif,quality_auto/wix4l_JPG.jpg)
![Eigenvalues calculated by Ti-84 plus](https://static.wixstatic.com/media/5887e2_5b4a941861a34819af553dd25915b859~mv2.jpg/v1/fill/w_114,h_44,al_c,q_80,usm_0.66_1.00_0.01,blur_2,enc_avif,quality_auto/wix5l_JPG.jpg)
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](https://static.wixstatic.com/media/5887e2_565a758a6d464758a71227f210e2f6b1~mv2.png/v1/fill/w_97,h_47,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_avif,quality_auto/Knipsel1_PNG.png)
![eigenvalues results by MatlabTi](https://static.wixstatic.com/media/5887e2_87701fb0b219405b8aa910b6f7d0adc1~mv2.jpg/v1/fill/w_92,h_194,al_c,q_80,usm_0.66_1.00_0.01,blur_3,enc_avif,quality_auto/wix6__JPG.jpg)
There is a 4X4 matrix example on :
Download the program eigenvalue.8xp:
Also second hand for low prices to benefit this program
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