Chapter 2
System of Linear Equations
• Existence and Uniqueness (2.2)
• Sensitivity and Conditioning (2.3)
January 14, 2010
Systems of Linear Equations
Example
Singularity and Nonsingularity
Existence and Uniqueness
Example: Nonsingularity
Example: NonSingularity
Geometric Interpretation
Illustration
How to define condition number of solving a linear
system?
Vector Norms
Example: Vector Norm
Properties of Vector Norms
Matrix Norm
Since A is linear, we can evaluate the max for ||x||=1
Illustration
Matrix Norms
Properties of Matrix Norms
Condition Number
Properties of Condition Number