# What is matrix reduction to normal form PAQ?

Here is my university syllabus. I started doing math in vacation just to get a head start because I am a dunce in math.

So, I began with chapter 2 - matrices - because it looked easier. I went half way through and got stuck at this part:

Rank of a matrix, reduction to
normal form PAQ, Linear dependence and independence of
rows/columns over a field.


I did go over Google and searched YouTube to see if I could find any reference material that would suit a novice but in vain.

Also, I am confused as to what these topics are. (Maybe because I did not find any good, detailed explanation)

Can you please provide me with:

1. A basic explanation of what these are
2. Reference to learning material ?

## 1 Answer

This is really a question about how to do an effective search; I suspect you may have tried to "kill a bunch of birds with one stone" by googling the entire phrase (all topics you list) in one search, since it was relatively easy to find a wealth of information for each of the topics you list. The only "tricky" part is understanding that "reducing a matrix to PAQ form" means expressing a normal matrix $N$ as the product $N = PAQ$ where exactly what the matrices $P, A, Q$ represent needs to be gleaned by reading the text. And reading the text is the best way to understand the concepts and terms you list! If you haven't acquired the class text/class notes, try to acquire those and review those in advance, if that's possible.

For a brief introduction to the terms you list, see the following links:

See also Linear Algebra, part of wikibooks. It's an online text for linear algebra which may serve you as a secondary reference as the need arises (the primary references being: your class text or notes, lectures, your instructor). Another freely distributed text is Hefferson's Linear Algebra (pdf).

• @Amzoti Thanks! Too many topics listed, most of them having chapters, even books addressing them, to try to "explain" in a meager math.se answer! Hopefully, some of the links will help with explanations and others to serve as references. – Namaste Jun 4 '13 at 1:21
• 1. I did try the video on PAQ form before I posted the question but the accent was hard to grasp. – Little Child Jun 4 '13 at 6:32
• @LittleChild That's very true. Try the pdf, perhaps. The key term to look for is "normal form". – Namaste Jun 4 '13 at 14:26
• Already done how to do row echelon, finished linear dependence and independence but I have a few questions. Maybe I will ask them in chat – Little Child Jun 4 '13 at 18:05
• I did go over wikipedia (computing rank of a matrix using row echelon section) on rank of a matrix. I did not find how it is related to linear dependence / independence. All it is related to is number of non-zero rows in row echelon. Did I miss anything? – Little Child Jun 4 '13 at 21:28