Linear Algebra and the C Language/a0p5

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00c.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RCA RC3 /* ------------------------------------ */ /* ------------------------------------ */ int main(void) { double a[RCA*RCA] ={ +2.363636363638, -1.909090909092, -0.272727272727, +1.818181818184, -1.545454545456, -0.363636363636, -0.909090909092, +1.272727272728, +1.181818181818 }; double NVN[RCA*RCA] ={ +0.784464540553, -0.408248290464, -0.557086014531, +0.588348405415, -0.408248290464, -0.742781352708, -0.196116135138, +0.816496580928, +0.371390676354 }; double **A = ca_A_mR(a, i_mR(RCA,RCA)); double **Nvn = ca_A_mR(NVN, i_mR(RCA,RCA)); double **invNvn = invgj_mR(Nvn, i_mR(RCA,RCA)); double **EValue = i_mR(RCA,RCA); double **T = i_mR(RCA,RCA); clrscrn(); printf(" A :"); p_mR(A, S9,P12, C4); printf(" Nvn :"); p_mR(Nvn, S9,P12, C4); printf(" Verify if:\n\n" " EValue = invNvn * A * Nvn\n\n" " EValue 1 EValue 2 EValue 3"); mul_mR(invNvn,A,T); mul_mR(T,Nvn,EValue); p_mR(EValue, S9,P12, C4); stop(); clrscrn(); printf(" A :"); p_mR(A, S9,P12, C4); printf(" Verify if:\n\n" " A = Nvn EValue invNvn"); mul_mR(Nvn,EValue,T); mul_mR(T,invNvn,A); p_mR(A, S8,P12, C3); stop(); clrscrn(); printf(" det(Nvn) = %.3e\n" " det(Nvn) != 0 V1 and V2 and V3 are linearly independent\n\n", det_R(Nvn)); printf(" The matrix A projects the space in the direction\n" " of the eigenvector V3 on a plan determined by\n" " the eigenvector V1 and V2 if :\n\n" " The eigenvector V1 has its eigenvalue equal to one and \n" " The eigenvector V2 has its eigenvalue equal to one and \n" " The eigenvector V3 has its eigenvalue equal to zero and \n\n" " If The vectors V1 and V2 and V3 are linearly independent\n\n"); stop(); f_mR(A); f_mR(Nvn); f_mR(invNvn); f_mR(T); f_mR(EValue); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ You verify the properties of the matrix A. * The values of the eigenvalues: EValue = invNvn A Nvn * The matrix: A = Nvn EValue invNvn * If the column vector of A are linearly independent Screen output example: A : +2.363636363638 -1.909090909092 -0.272727272727 +1.818181818184 -1.545454545456 -0.363636363636 -0.909090909092 +1.272727272728 +1.181818181818 Nvn : +0.784464540553 -0.408248290464 -0.557086014531 +0.588348405415 -0.408248290464 -0.742781352708 -0.196116135138 +0.816496580928 +0.371390676354 Verify if: EValue = invNvn * A * Nvn EValue 1 EValue 2 EValue 3 +1.000000000000 +0.000000000000 +0.000000000000 +0.000000000000 +1.000000000000 +0.000000000000 -0.000000000000 +0.000000000000 +0.000000000000 Press return to continue. A : +2.363636363638 -1.909090909092 -0.272727272727 +1.818181818184 -1.545454545456 -0.363636363636 -0.909090909092 +1.272727272728 +1.181818181818 Verify if: A = Nvn EValue invNvn +2.363636363638 -1.909090909092 -0.272727272727 +1.818181818184 -1.545454545456 -0.363636363636 -0.909090909092 +1.272727272728 +1.181818181818 Press return to continue. det(Nvn) = 1.635e-01 det(Nvn) != 0 V1 and V2 and V3 are linearly independent The matrix A projects the space in the direction of the eigenvector V3 on a plan determined by the eigenvector V1 and V2 if : The eigenvector V1 has its eigenvalue equal to one and The eigenvector V2 has its eigenvalue equal to one and The eigenvector V3 has its eigenvalue equal to zero and If The vectors V1 and V2 and V3 are linearly independent Press return to continue.