Do you know whether boost has functions that can calculate the determinant and the inversion of a complex matrix? The matrix dimension isn't large (less than 50).
Inversion: Input: matrix M = A +i*B with A,B two real matrices of dimension (n x n) with n <50.
Output:
I googled but didn't succeed.
Thank you in advance.
Finally I know why these operators on inversion and determinant of matrices aren't implemented. It's because we have closed-form solution of these 2 operators from classical operators on real matrices.
For matrix inversion: we have this closed-form solution https://fr.mathworks.com/matlabcentral/fileexchange/49373-complex-matrix-inversion-by-real-matrix-inversion
For matrix determinant, we have:
det((A+iB))= det (A * (I + i A1.B)) (with A1 is the inversed matrix of A)
= det(A) * det (I + i A1.B))
= det(A) * det (U1 (I + iD) U2) (with U1 = A1.B, U2 is the invered matrix of U1, D is the diagonal matrix of U1) = det(A) *det(I +iD). It's easy to calculated the determinant of I +iD which is a diagonal matrix.
So, det(A+iB) = det(A) * det(I +iD) with D: the matrix of eigenvalues of (A^(-1) * B)