Is there a command which will row reduce a matrix, but not into echelon form and abides by the following rule:
-The only reduction operation is Ri + cRj -> Ri where c is some constant, Ri is the ith row which will receive the reduction and Rj is the jth row.
So, this means no row swapping, or constant multiplied by the row receiving the reduction.
The goal is to classify a matrix as PD,SPD, Indefinite, etc. by upper-traingularizing the matrix.
(Is Uppertriangularize[m] the proper function?)
I wish I knew the name of this method to better-search for what I need.
I need this for graduate-level Optimization class. The university uses MATLAB, and the professor suggests that there's a function to do this (we don't need to prove or show work that we can row-reduce at this level of mathematics). Having used Mathematica in my undergraduate, I'd hate to switch over, or take the time to learn MATLAB after getting acquainted with Mathematica.