All bilinear terms:

index_1.gif

Multiplication result:

index_2.png

index_3.png

index_4.png

All monomials that are to be represented in matrix multiplication

index_5.gif

index_6.png

Listing of all bases found by C++ program mentioned earlier:

index_7.png

index_8.png

index_9.png

index_10.png

index_11.png

index_12.gif

index_13.png

index_14.png

index_15.png

Some equation samples:

index_16.png

c[1,1] r[1,1] x[1,1]+c[3,1] r[3,1] x[1,3]==1
c[3,2] r[3,1] x[1,3]+c[5,2] r[5,1] x[1,5]==0
c[1,3] r[1,1] x[1,1]+c[2,3] r[2,1] x[1,2]+c[5,3] r[5,1] x[1,5]==0
c[2,3] r[2,2] x[1,2]+c[7,3] r[7,2] x[1,7]==1
c[7,4] r[7,2] x[1,7]==0

index_17.png

index_18.png

index_19.png

index_20.png

index_21.png

Verifies that selected bases can be taken with signs specified by x[i,j] to produce the same monomials as matrix multiplication.

index_22.gif

index_23.png

index_24.png

index_25.png

index_26.png

Created with the Wolfram Language