This is an example I got about eigenvalues...

Maybe a specific example, suppose you have the matrix A:

[ 2 4 ]

[ 3 5 ]

We turn this into the matrix A-xI

[ 2-x 4 ]

[ 3 5-x]

This has determinant det (A-xI) = (2-x)(5-x)-(3)(4) = x^2-7x-2. You can then solve this quadratic equation using whatever method you like to use to solve quadratic equations. Note: you did this in your linear algebra class, so dig that book back out.

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Here is my code:

Code:#include <stdio.h> int main() { float a[2][3], b[2][1], mean[2][1], after[2][3], afterT[3][2], cov[2][2]; int i, j, k, h, p; printf("\nEnter three 2D vectors in form of 2x3 matrix A: "); for(i=0; i<2; i++) { for(j=0; j<3; j++) { printf("\n Enter a[%d][%d]: ", i,j); scanf("%f", &a[i][j]); } } /*Compute the Mean*/ b[0][0]= a[0][0]+a[0][1]+a[0][2]; b[1][0]= a[1][0]+a[1][1]+a[1][2]; for(i=0; i<2; i++) { for(j=0; j<1; j++) { mean[i][j]= b[i][j]*(1.0/3.0); } } /*Subtract each vector by the mean vector*/ for(i=0; i<2; i++) { for(j=0; j<3; j++) { for(k=0; k<1; k++) { after[i][j]=a[i][j]-mean[i][k]; } } } /*Transpose after (afterT)*/ for(i=0; i<2; i++) { for(j=0; j<3; j++) { afterT[j][i]=after[i][j]; } } /*Compute and Display Covariance*/ cov[0][0]= (after[0][0]*afterT[0][0])+(after[0][1]*afterT[1][0])+(after[0][2]*afterT[2][0]); cov[0][1]= (after[0][0]*afterT[0][1])+(after[0][1]*afterT[1][1])+(after[0][2]*afterT[1][2]); cov[1][0]= (after[1][0]*afterT[0][0])+(after[1][1]*afterT[1][0])+(after[1][2]*afterT[2][0]); cov[1][1]= (after[1][0]*afterT[0][1])+(after[1][1]*afterT[1][1])+(after[1][2]*afterT[2][1]); cov[0][0]=(.5)*cov[0][0]; cov[0][1]=(.5)*cov[0][1]; cov[1][0]=(.5)*cov[1][0]; cov[1][1]=(.5)*cov[1][1]; printf("\n Their product is :\n"); for(i=0; i<2; i++) { for(j=0; j<2; j++) { printf("%.1f ", cov[i][j]); } printf("\n"); } /*Determinants*/ cov[0][0]=cov[0][0]-x; cov[1][1]=cov[1][1]-x; det=(cov[0][0]*cov[1][1])-(cov[1][0]*cov[0][1]) return(0); }

The thing I can't figure out is because the eigenvalues are the roots of the determinant, how to compute the eigenvalues...As seen above I have variable "det" as the determinant of the 2x2 covariance matrix....

can someone help? thanks

PS- I can only use the library functions sqrt, printf, scanf