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Linear Algebra and the C Language/a0gm
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Similar matrices:
In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that : B = InvP A P... Wikipedia: Matrix similarity
Create similar matrices: B = InvP A P
First, I create the matrix P and its inverse.
for(i=A0; i<ARRAY; i++)
{
A[i] = i_mR(RCA,RCA);
P[i] = r_mR( i_mR(RCA,RCA),99);
InvP[i] = inv_mR(P[i], i_mR(RCA,RCA));
}
For A[0], I choose a symmetric matrix so that the eigenvalues are real.
rsymmetric_mR(A[0],99);
I am currently creating all the similar matrices.
for(i=A0; i<(ARRAY-C1); i++)
{
mul_mR(InvP[i],A[i],T);
mul_mR(T,P[i],A[i+C1]);
}
Similar matrices have the same determinant.
c00a.c ... ... ... ... (2) c00a.c
Similar matrices have the same trace.
c00b.c ... ... ... ... (2) c00b.c
Similar matrices have the same eigenvalues.
c00c.c ... ... ... ... (2) c00c.c
IF ... A[1] = InvP A[0] P ... Then ... A[1]**3 = InvP A[0]**3 P
c00d.c
IF ... A[1] = InvP A[0] P ... Then ... InvA[1] = InvP InvA[0] P
c00e.c