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LINEAR ALGEBRA (MATH 317H) CASIM ABBAS
 

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) =

  

Source: Abbas, Casim - Department of Mathematics, Michigan State University

 

Collections: Mathematics