ABSTRACT
An m-multilinear functional on Rn is a real-valued function
M(a1, . . . ,am), a1, . . . ,am ∈ Rn,
that is linear in each variable ai separately. (See Section 9.7.) Such a function is said to be alternating if interchanging two vectors changes the sign of M :
M(a1, . . . ,ai, . . . ,aj , . . . ,am) = −M(a1, . . . ,aj , . . . ,ai, . . . ,am).
