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Mutual inductance matrix gives the quantitative estimation of the mutual magnetic affect of the conductors in the system. In practical engineering the field distribution in the system of conductors is replaced by the equivalent electric circuit consisting of inductances.
This equivalent schema operates with currents, fluxes and induction coefficients that comprise the mutual inductance matrix:

(1) 
where
Ψ_{k}  kconductor flux linkage,
I_{k}  kconductor current,
a_{ij}  self and mutual inductances.
The matrix is symmetrical, i.e. a_{ij} = a_{ji}.
Additional links on this subject:
Mutual inductance from Wikipedia, the free encyclopedia.