01.25.06
From Vectorcalcumb
Revision as of 01:22, 17 February 2006 by 68.160.168.24 (Talk)
Multilinear transform: Let <m>V</m> be a vector space. A function <m>f:V^n right F</m> is called multilinear if for <m>i=1,2,cdots,n</m> we have <m>cf(v_1,cdots,v_i,cdots,v_n) = f(v_1,cdots,cv_i,cdots,v_n)</m> and <m>f(v_1,cdots,v_i,cdots,v_n) + f(v_1,cdots,v_i prime,cdots,v_n) = f(v_1,cdots,v_i+v_i prime,cdots,v_n)</m>.
Examples are determinants, dot-products, and cross-products.
