Let f: X Ã Y be a bilinear functional on finite-dimensional linear spaces X and Y. Let m = dim X and n = dim

Let f: X × Y †’ „œ be a bilinear functional on finite-dimensional linear spaces X and Y. Let m = dim X and n = dim Y. For every choice of bases for X and Y, there exists an m × n matrix of numbers A = (aij) that represents f in the sense that

for every x ˆŠ X and y ˆŠ Y

fK.) - 4) f(x,y) aijXiyj i=l j=l