 
Summary: LINEAR ALGEBRA (MATH 317H)
CASIM ABBAS
Assignment 17  inner product spaces, norms
(1) Let x = (1, 2i, 1 + i)T
and y = (i, 2  i, 3)T
be vectors in C3
(endowed with
the standard inner product). Compute
(a) (x, y) , x , y
(b) (3x, 2iy) , (2x, ix + 2y)
(c) x + 2y
After part (a) you can complete parts (b) and (c) using the properties of
the inner product without computing the vectors involved.
(2) Explain why each of the following is not an inner product on the given
vector space
(a) (x, y) = x1y2  x2y1 on R2
where x = (x1, x2)T
, y = (y1, y2)T
(b) (A, B) = trace(A + B) on the space of real 2 × 2 matrices
(c) (f, g) =
