MAT 4725Numerical Analysis
Section 7.1 Part I
Norms of Vectors andMatrices
http://myhome.spu.edu/lauw
Chapter 7 Iterative Techniquesin Matrix Algebra
Section 2.2 Fixed-Point Iteration
Chapter 7 Iterative Techniquesin Matrix Algebra
Section 7.3 Iterative Techniques
Chapter 7 Iterative Techniquesin Matrix Algebra
Section 7.3 Iterative Techniques
Chapter 7 Iterative Techniquesin Matrix Algebra
Section 7.3 Iterative Techniques
Chapter 7 Iterative Techniquesin Matrix Algebra
Section 7.3 Iterative Techniques
We need a way tomeasure the distancebetween two vectors
7.1 Norms of Vectors andMatrices
Norms on real vector space (Part I)
Norms on Matrices (Part II)
n Dimensional Real VectorSpace
Linear Algebra, Mult. Variables Calculus
Applied Analysis
Definition 7.1
l2 Norm (Euclidean Norm)
Usual distance function on
l2 Norm (Euclidean Norm)
Usual distance function on
Geometric Interpretations of
l Norm
Geometric Interpretations of
Example 1
Theorem 7.3(Cauchy-Schwarz Inequality)
l2 Norm is a vector norm
Proof:
Definition 7.4
Definition 7.5
Theorem 7.6+7.7
Example 2
Classwork
Homework
Download HW.
Read 7.1 (skip all the proofs)