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: 


*

*A basic explanation of what these are  

*Reference to learning material ?

 A: 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:


*

*Wikipedia Rank of a Matrix Note this is closely related to determining linear independence of the rows/columns of a matrix.

*Video: Reducing matrix to "PAQ" Form

*pdf: Normal form of a matrix $N = PAQ$

*Wikipedia Linear Independence (vectors/matrices)

*Khan Academy Introduction to Linear Dependence and Independence
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).
