Linear Algebra and the C Language/a0n8

__NOTOC__ The spectral decomposition: The matrix A and the inverse matrix of A have the same eigenvectors but arranged in reverse order c00a.c ... ... ... ... ... ... Octave The application b1r1 + b2r2 + b3r3 = Ide (The b_r_ are projectors.) c00b.c ... ... ... ... ... ... Octave b*: The columns of the eigenvectors of A r*: The rows of eigenvectors of the inverse of A E1 b1r1 + E2 b2r2 + E3 b3r3 = A c00c.c ... ... ... ... ... ... Octave E*: The eigenvalues of A b1r1**2 = b1r1; ... ... ... b1r1**3 = b1r1; ... ... ... b1r1**P = b1r1; c00d.c ... ... ... ... ... ... Octave Several consecutive projections, (b_r_**P), give the same result b1r1 * b3r3 = 0; ... ... ... b1r1 * b2r2 = 0; ... ... ... b2r2 * b3r3 = 0; c00e.c ... ... ... ... ... ... Octave The projectors b_r_ are orthogonal to each other E1**2 b1r1 + E2**2 b2r2 + E3**2 b3r3 = A**2 c00f.c ... ... ... ... ... ... Octave Calculate the power n of A with the power n of each of the eigenvalues 1/E1 b1r1 + 1/E2 b2r2 + 1/E3 b3r3 = inv(A) c00g.c ... ... ... ... ... ... Octave Calculate the inverse of A with the inverse of each of the eigenvalues