Question: A function f: Rn x Rm Rp is bilinear if for x,x1, x2 R n, y,y1, y2 Rm and a R We
We have,
f(ax, y) = af (x, y) = f(x, ay)
f(x1 + x2, y) = f(x1, y) + f(x2, y)
f(x, y1 +y2) = f(x, y1) + f(x, y2)
(a) Prove that if f is bilinear, then
(b) Prove that Df (a, b) (x, y) = f (a,y) + f(x,b).
(c) (Show that the formula for Dp (a, b) in theorem 2-3 is a special case of (b
Step by Step Solution
★★★★★
3.54 Rating (157 Votes )
There are 3 Steps involved in it
1 Expert Approved Answer
Step: 1 Unlock
We have Prove that if is bilinear then Let have a 1 in the ... View full answer

Question Has Been Solved by an Expert!
Get step-by-step solutions from verified subject matter experts
Step: 2 Unlock
Step: 3 Unlock
Document Format (1 attachment)

M-C-12.docx
120 KBs Word File