Linear Algebra and the C Language/a0n1

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as: c00a.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ void fun(int r) { double **A = rsymmetric_mR( i_mR(r,r),9); double **InvA = invgj_mR(A, i_mR(r,r)); double **AEVect = eigs_V_mR(A, i_mR(r,r)); double **InvAEVect = eigs_V_mR(InvA, i_mR(r,r)); clrscrn(); printf(" A:"); p_mR(A, S10,P4,C6); printf(" InvA:"); p_mR(InvA, S10,P4,C6); stop(); clrscrn(); printf(" The matrix A and the matrix InvA\n" " have the same Eigenvectors. They \n" " are in reverse order. \n\n\n" " The eigenvectors of A being \n" " an orthonormal matrix, we \n" " will simply take its transpose \n" " as inverse in the next files. \n\n" " EigenVector of A:"); p_mR(AEVect,S10,P4,C6); printf(" EigenVector of InvA:"); p_mR(InvAEVect,S10,P4,C6); f_mR(A); f_mR(InvA); f_mR(AEVect); f_mR(InvAEVect); } /* ------------------------------------ */ int main(void) { time_t t; srand(time(&t)); do { fun(R3); } while(stop_w()); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ To calculate the spectral decomposition of matrix A. We need the eigenvectors and eigenvalues ​​of matrix A and the eigenvectors of the inverse of A. The eigenvectors of the inverse of A are identical to the eigenvectors of A but not in the correct order. (Try the example) To obtain the eigenvector rows of the inverse of A, I will take the transpose of the eigenvectors of A, since A and the inverse of A have the same eigenvectors, only when A is symetric. Screen output example: A: -5.0000 +4.0000 -2.0000 +4.0000 +2.0000 -2.0000 -2.0000 -2.0000 +5.0000 InvA: -0.0698 +0.1860 +0.0465 +0.1860 +0.3372 +0.2093 +0.0465 +0.2093 +0.3023 Press return to continue. The matrix A and the matrix InvA have the same Eigenvectors. They are in reverse order. The eigenvectors of A being an orthonormal matrix, we will simply take its transpose as inverse in the next files. EigenVector of A: -0.3066 +0.9159 +0.2592 -0.5409 -0.3917 +0.7443 +0.7832 +0.0881 +0.6155 EigenVector of InvA: +0.2592 +0.9159 -0.3066 +0.7443 -0.3917 -0.5409 +0.6155 +0.0881 +0.7832 Press return to continue Press X return to stop