balancing of pair of symmetric matrices
T = equil(P, Q)
two positive definite symmetric matrices
nonsingular matrix
equil returns t such that:
equil
t
T*P*T' and inv(T)'*Q*inv(T) are both equal to a same diagonal and positive matrix.
T*P*T'
inv(T)'*Q*inv(T)
P=rand(4,4);P=P*P'; Q=rand(4,4);Q=Q*Q'; T=equil(P,Q) clean(T*P*T') clean(inv(T)'*Q*inv(T))