Le Ei, i = 1,., k be Euclidean spaces of various dimensions. A function f: E1 X. X Ek→Rp is called multi linear if for each choice of xj € Ej, j ≠ I the function f: Ei→Rp defined by g(x) = f(x1,.,xi-1, x,xi +1, ., xk) is a linear transformation.
(a) If is multi linear and i ≠ j, show that for (h=(h1, ., hk), with hi € Ei, we have
Prove that
(b) Df (a1,., ak) x1, ., xk) = =1 f(a1,., ai-1, xi, ai+1,., ak)