MATH307-Individual Homework 9 Solved

1.   Write down the default inner product in C3 and show that the induced norm corresponding to this default inner product is actually the 2-norm. Let

Ñ1+ ié Ñ 1 é u = 2i ,v = 3− i ,

                                                                                   3+ i                         −i

find the norm of u and the distance between u,v under the default inner product in C3.

2.   Find the 1−,2−,∞− norm unit balls in R2 and sketch them. Find all the x ∈R2 that satisfies kxk1 =kxk2 =kxk∞=1.