L. Vandenberghe
EE133A
11/10/14
Midterm solutions
Problem 1. The trace of a square matrix is the sum of its diagonal elements. What is the
complexity (number of ops for large n) of computing the following quantities?
1. The trace of AB, where A and B are
L. Vandenberghe
EE133A
11/19/2014
Homework 5 solutions
1. Circulant Toeplitz matices.
(a) For k = 1, the result is obvious because S k1 and diag(W e1 ) are the nn identity
matrix.
The columns of W S k1 are the columns of W , shifted circularly to the left
L. Vandenberghe
EE133A
11/10/2015
Homework 5 solutions
1. Exercise 8.2.
(a) We use x1 = log and x2 = t0 log as variables, and consider the conditions
log ni ti log t0 log = t1 x1 x2 ,
i = 1, . . . , 13.
The least-squares estimate for x1 and x2 is the solu