APPLIED LINEAR ALGEBRA
HW1
HAMED NIKBAKHT
Exercise 1.3
Because R is non-singular then Range (R)= Cn and it is invertible matrix. Thus, the columns of R must be
linearly independent.
R is also upper-triangle; then, the first n columns of R are in the span

Solutions to Homework 3, Math 575A Fall 2008
5.2 Consider an arbitrary m n matrix A. Such a matrix has full rank if and only if all of
its singular values are positive. Decompose A = U V . Construct a sequence of matrices
Ak = U k V , where k is a diagona

Chapter 2
Sensitivity, Errors and
Norms
Two difficulties arise when we solve systems of linear equations or perform other
matrix computations:
(i) Errors in matrix elements.
Matrix elements may be contaminated with errors from measurements or previous com

Lecture16
March 13, 2008
Lecture 16: Numerical Linear Algebra
Outline
0) Newton Demo for Linear systems:
1) Overview of Linear Algebra
2) Basics: Vector and Matrix Norms
3) The condition number of a matrix cond(A)
4) The condition number and error estimat

5.2 Matrix Norms
281
1
max Ax = A
x=1
A
min Ax =
x=1
1
A -1
Figure 5.2.1. The induced matrix 2-norm in 3 .
Intuition might suggest that the euclidean vector norm should induce the
Frobenius matrix norm (5.2.1), but something surprising happens instead.
M

UNF Digital Commons
UNF Theses and Dissertations
2010
Matrix Singular Value Decomposition
Petero Kwizera
University of North Florida
Suggested Citation
Kwizera, Petero, "Matrix Singular Value Decomposition" (2010). UNF Theses and Dissertations. Paper 381.