Python: Inverse matrix of an 2n x 2n matrix

Can anyone help me in finding an inverse matrix on 2n x 2n matrix such that for i,j=1,2,...,n ,

-m_(ji) , for a_(ij) entry and i ≠ j ,

sum_(i ≠ k) m_(ik) + (y_i + p_i*t_i) , for a_(ii) entry and k=1,2,..,n ,

-p_i*t_i , for a_((n+i)i) entry , and

d_i , for a_((n+i)(n+i)) entry.

I tried for i=2, and 3, but when I tried i=4, my program wont end. Here is my program:

    from sympy import *      from numpy import matrix      from numpy import linalg      from sympy import Matrix        Ab, Ac, Ad, Ba, Bc, Bd, Ca, Cb, Cd, Da, Db, Dc, Za, Zb, Zc, Zd, Xa, Xb,       Xc, Xd, Ya, Yb, Yc, Yd = symbols('Ab, Ac, Ad, Ba, Bc, Bd, Ca, Cb, Cd, Da,       Db, Dc, Za, Zb, Zc, Zd, Xa, Xb, Xc, Xd, Ya, Yb, Yc, Yd')      V = Matrix([[Ab+Ab+Ad+Za, -Ba, -Ca, -Da, 0, 0, 0, 0],          [-Ab, Ba+Bc+Bd+Zb, -Cb, -Db, 0, 0, 0, 0],          [-Ac, -Bc, Ca+Cb+Cd+Zc, -Dc, 0, 0, 0, 0],          [-Ad, -Bd, -Cd, Da+Db+Dc+Zd, 0, 0, 0, 0],          [-Xa, 0, 0, 0, Ya, 0, 0, 0],          [0, -Xb, 0, 0, 0, Yb, 0, 0],          [0, 0, -Xc, 0, 0, 0, Yc, 0],          [0, 0, 0, -Xd, 0, 0, 0, Yd]])      V_inverse = V.inv()      print("V'=", V_inverse)  

Here, I substitute m_(12) = Ab, m_(13) = Ac, m_(14) = Ad,

m_(21) = Ba, m_(23) = Bc, m_(24) = Bd,

m_(31) = Ca, m_(32) = Cb, m_(34) = Cd,

m_(41) = Da, m_(42) = Db, m_(43) = Dc,

y_1 = Ya, y_2 = Yb, y_3 = Yc, y_4 = Yd,

p_1t_1 = Xa, p_2t_2 = Xb, p_3t_3 = Xc, p_4t_4 = Xd.

Thank you.

https://stackoverflow.com/questions/67322498/python-inverse-matrix-of-an-2n-x-2n-matrix April 30, 2021 at 01:40AM