Linear Algebra and the C Language/a0n8

Matrix A and the inverse matrix of A have the same eigenvectors but arranged in reverse order

• c00a.c

b1r1 + b2r2 + b3r3 = Ide (The b_r_ are projectors.)

• c00b.c
  • 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
  • E*: The eignvalues of A

b1r1**2 = b1r1; ... ... ... b1r1**3 = b1r1; ... ... ... b1r1**P = b1r1;

• c00d.c
  • Several consecutive projections, (b_r_**P), give the same result

b1r1 * b3r3 = 0; ... ... ... b1r1 * b2r2 = 0; ... ... ... b2r2 * b3r3 = 0;

• c00e.c
  • The projectors b_r_ are orthogonal to each other

E1**2 b1r1 + E2**2 b2r2 + E3**2 b3r3 = A**2

• c00f.c
  • 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
  • Calculate the inverse of A with the inverse of each of the eigenvalues