INTER-RELATIONSHIP BETWEEN VARIOUS MATRICES

In this section,we will be discussing about the relationship between different matrices like incidence matrix(A),Tie-set matrix or Fundamental loop matrix(B) and Cut-set matrix(Q).

A=[A_t:A_l]  where, A_t means matrix of twigs and A_l  means matrix of links

B=[B_t:B_l] where , B_t means matrix of twigs and B_l means matrix of links

                 But for a fundamental loop matrix B_l =U,where U is the identity matrix.

Q=[Q_t:Q_l] where they have the usual meaning as stated above

RELATIONSHIP BETWEEN INCIDENCE MATRIX A AND FUNDAMENTAL LOOP MATRIX B:

We know that A and B are orthogonal.So

                                                   AB^T=0

[A_t:A_l]*B_t^T =0

              U

So A_tB_t^T+A_l=0   or    B_t^T=A_t^-1A_l

B_t= [ -A_t^-1 A_l ]^T

RELATIONSHIP BETWEEN A AND Q:

AI_b = 0     or      QI_b = 0

From this relation,we will get

Q_l = A_t^-1 A_l