APPLIED LINEAR ALGEBRA
Because R is non-singular then Range (R)= Cn and it is invertible matrix. Thus, the columns of R must be
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
Sensitivity, Errors and
Two difficulties arise when we solve systems of linear equations or perform other
(i) Errors in matrix elements.
Matrix elements may be contaminated with errors from measurements or previous com
March 13, 2008
Lecture 16: Numerical Linear Algebra
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
max Ax = A
min Ax =
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.
UNF Digital Commons
UNF Theses and Dissertations
Matrix Singular Value Decomposition
University of North Florida
Kwizera, Petero, "Matrix Singular Value Decomposition" (2010). UNF Theses and Dissertations. Paper 381.