CS206 Problem Set 2
1. NLA 6.1
SOLUTION:
(I 2P )(I 2P ) = I 4P + 4P 2 = I
2. NLA 6.4
SOLUTION: Given a matrix A, the orthogonal projector onto the range of A can be
expressed by the formula:
P = A(A A)1 A
Using this formula, we have:
(a) The orthogonal pr

Solutions to Homework 6, Math 575A Fall 2008
11.1 a) If x = A+ b, then Ax = P b is the orthogonal projection of b onto the range of A.
|A+ | = supb |A+ b|/|b| supb |A+ b|/|P b| since we know that |P b| |b|, (|P | 1).
However, supb |A+ b|/|P b| supx |x|/|A

Solutions to Homework 5, Math 575A Fall 2008
9.1
Error due to discretization for Legendre Polynomials
0.1
0.08
0.06
0.04
Error
0.02
0
0.02
0.04
0.06
0.08
0.1
1
0.5
0
x
0.5
1
The code below generated the gure, and produced values of the innity norm of the

Computational math: Assignment 2
Thanks Ting Gaos support for this HW solutions.
5.2 Using the SVD, prove that any matrix an Cmn is the limit of a sequence
of matrices of full rank. In other words, prove that the set of full-rank matrices is
a dense subse

Solutions to Homework 2, Math 575A Fall 2008
3.2 The spectral radius (A) is the maximum of the absolute values of the eigenvalues of A.
Suppose is an eigenvalue of A. Then there is a nonzero vector v so that Av = v, and so,
for any norm | |, |Av| = |v| =

Homework 1
Elena Davidson
CS 106
Spring 2004
8 April 2004
Problem 1.1
Let B be a 4 4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each

Homework 2 solutions
September 24, 2009
Lecture 3
Problem 3.1
1. x
W
0, and x
W
x
W
3. x
= | x
= 0 only if x = 0
W
W
+ y
W
or
ia
2. x + y
W
Ho
wl
e
We want to show that x W = W x is a norm when is a norm. So we just need to show that
W obeys the three