Gaussian Reduction v1
(C) 2001 Bennett S. Kalafut

Performs the forward elimination (O1,A) and full Gaussian reduction (O,U) procedures on a matrix M.

O1(M)=A
O(M)=U

O1 and O are the products of the elementary matrices which perform (respectively) the forward and full Gaussian reduction processes.  Note that if M is square and invertable O will be its inverse.


**Command Line Syntax**
gauss(M)

**Use**
This is fairly self-explanatory.  Enter variable names into the fields of the dialog box.  Variable names must follow standard TI-89 conventions, otherwise an error message will be returned.

**Miscellany**
The naming conventions O1, A, O, and U are taken from Terry Lawson's "Linear Algebra".  There are probably others out there but it's the terminology I'm used to.

I attempted to write this as a void function of sorts, which would give the values as side-effects, but TI-Basic is a "bondage and discipline" language of sorts and does not have as loose a definition of a function as, for example, C.  Whether or not these restrictions are artificial (they seem like it!) I do not know; increased flexibility in programming is on my wish list for the next TI calculator.

**Contact**
If you have any questions, comments, or concerns feel free to e-mail me at bkalafut@bigfoot.com

**License**
Distribution of this program is released to the public domain on the following condidions.

1)  That this text file accompany all distribution of the program.
2)  That this program not be included in any CD-Rom, print, or similar offline collection intended for distribution without my expressed written consent.

**Final Word**
Uses of this program are few and far between.  For everyday solution to systems of linear equations, the standard "rref(" command will do.  If you are taking a linear algebra class, however, or otherwise need the matrices O and O1, this will be useful.

Another program you might find useful is the Fundamental Subspaces Toolbox which is archived at http://www.ticalc.org/pub/89/basic/math/fundspace.zip  This contains functions for the rank, nullity, row space, range, null space, and null space of the transpose of a matrix.

Until then, I hope all is well with you and your studies.  Don't just do math:  Study math, come to understand math, teach math.

Re-legalize freedom and show your faith in people.  Vote Libertarian!  http://www.lp.org

Peace,
Ben Kalafut