LU Decomposition

[Luke Setzer]

I keep running the LU decomposition function on the TI-Nspire CAS
software and the results differ from those in the textbook. I cannot
understand the function of the p matrix in the result. Before I post
a lengthy example, perhaps someone can enlighten me in a few words.

[Nelson Sousa]

The P matrix is a permutation matrix. What it does is switch lines (I
don't know what are the criteria to switch lines). Check your
reference guide, it will probably tell you in greater detail what do
those matrices mean.

Cheers,
Nelson

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[Wayne]

With respect to obtaining a different answer than the textbook, the LU
decomposition is not unique in general; so under some circumstances
different answers may be obtained depending on the method of
calculation. I do not remember the conditions on the matrix for
uniqueness of its decomposition but I think all the cofactors of the
main diagonal have to be non-zero. Don't quote me on that, but the
exact conditions should be in a linear algebra textbook (at least the
older ones).
Wayne

[Luke Setzer]

Okay, so I was able to write a small function program that swaps rows
of L based on P so that LU equals the original matrix. Now I just
need to find a way to force the LU function to give me the same
answers as the textbook. Meh!

[Wayne]

There is no need for a separate function, just multiply by P inverse
since (P inverse)*L*U is the original matrix. Of course (P inverse)*L
is no longer lower triangular in the general case.
Wayne

[Luke Setzer]

That was very helpful! Thanks! Now if someone could please explain
why the calculator does this rather than simply return a straight L
and U, that would help even more.