Chapter 4: Numerical Linear Algebra
The following sections are included:
Linear Dependence, Independence of Sets of Vectors
Rank and Bases for a Set of Vectors
Two Algorithms to Check Linear Dependence, Find Rank and a Basis for a Given Set of Vectors
How to Get an Alternate Basis by Introducing a Nonbasic Vector into A Basis?
The Rank of a Matrix
Computing the Inverse of a Nonsingular Square Matrix Using GJ Pivot Steps
Pivot Matrices, Elementary Matrices, Matrix Factorizations, and the Product Form of the Inverse
How to Update the Inverse When a Column of the Matrix Changes
Results on the General System of Linear Equations Ax = b
Optimization, Another Important Distinction Between LA, LP, and IP; and the Duality Theorem for Linear Optimization Subject to Linear Equations
Memory Matrix Versions of GJ, G Elimination Methods
Orthogonal and Orthonormal Sets of Vectors, Gram–Schmidt Orthogonalization, QR-Factorization, Orthogonal Matrices, Orthonormal Bases
Additional Exercises
References
