Tutorials about Linear Algebraic Systems of Equations (aka Matrix Problems)

Introductory information

-          Here is an Introduction to linear algebraic algebraic equation systems.

-          Here is an Introduction to matrix theory (adapted from University of Melbourne)

-          What is hard about solving linear algebraic equation systems?

-          What do the Solve* programs do with all these difficulties?

Technical Details on Solving Linear Systems

-          How are linear algebraic equation systems solved? Part 1:Elimination and Back Substitution

-          How are linear algebraic equation systems solved? Part 2: Using an LU Decomposition

-          How are linear algebraic equation systems solved? Part 3: Using an SVD Decomposition

-          How are linear algebraic equation systems solved? Part 4: About Ill-Conditioned Problems

Details

-          You can read details about the regularization methods used in Solve* in How to handle ill-conditioning.

-          You can learn how equality and inequality constraints are handled in How to handle constraints.

-          See what the Picard Condition is all about in What is the Picard Condition?

-          You may want to know about How the Condition Number Affects Solution Accuracy.

Further Details

There is a lot of material available on the web on the topic of matrices, especially introductory material. The following material is unusually detailed on topics related to matrix theory, machine arithmetic, etc.

1.       About Gaussian Elimination

2.       Norms and Condition Numbers

3.       Error Bounds and Residuals

These three files are part of a set of course notes available at http://www.cse.iitd.ernet.in/~dheerajb/CS210.htm .