Thursday, August 23, 2012

Linear Algebra

Last night I spent close to an hour studying 2 sections of the book, then spent another hour watching the video lesson covering those two sections.  Today I spent about an hour on the homework on those two sections.

And that was just Linear Algebra.  Statistical Analysis is another animal entirely!

Yes, I brought this upon myself--I could be done with this degree in 10 months if I just wanted to jump through hoops at National or Phoenix, but that isn't the point of this post.

As an undergrad I took linear algebra while an exchange cadet at the Air Force Academy.  A recent retiree from my school was the course director for linear algebra at USAFA for a couple of years immediately before I got there--talk about a coincidence!  Anyway, I once talked to him about what a horrible course it was, how the book was horrible, and he was horrified.  He said it was a wonderful book, then pulled it out of his closet (!!!) and asked what was wrong with it.  "This isn't the book we used," I said.  The next day I brought in the book we had used, he glanced through it and said, "It's no wonder you didn't learn anything.  This is way above the head of anyone taking an introductory linear algebra course.  This is at least master's level."

I got the highest score in the class and there's an A on my transcript, but if I remember correctly, that score was maybe a 60% or something.  I could go through some motions but I didn't learn a thing.  Last night and today I learned Gaussian Elimination, how to manipulate matrices into reduced row-echelon form and solve systems of equations.

I've learned more in 3 hours of this course than I learned in a semester in my previous Linear Algebra course.

Now I need to tackle some of the other course.


Alf Tupper said...

I like Gilbert Strang's books - both his Calculus and Linear Algebra books
are excellent. Check them out at MIT:

Joshua Sasmor said...

I agree - Strang's books are good. I teach my intro course out of Anton's book.

Anonymous said...

Real-world application: Linear Algebra is used in frame transformations. Here's an example.

Suppose a plane's radar picks up a target. From the plane, the target is bearing xxx, distance yyy. Need to tell a ground-based radar to look at the target. How? xxx, yyy from the plane's location is meaningless to the ground radar, which is in a completely different location.

Turns out, it's done via matrix multiplication. The plane's location (from gps) is known. There is a conversion matrix from that location to another frame, say Earth Centered, Earth Fixed. One matrix multiply, and now the target's location is expressed in relation to the ECEF frame. Feed that to the ground radar, it does another matrix multiply from ECEF to its known location, and poof, the ground radar now has a bearing to the target.

All done with linear algebra. Math is fun!

PeggyU said...

Darned if I remember anything from the linear algebra course I took in college. However, we did use augmented matrices to solve systems of equations in the precalc class I took in high school. I still remember how to do Gaussian reduction. I also remember finding the inverses of matrices that way. That's what comes of being so old, I guess. :) Calculators just weren't as fancy back then!

Anonymous said...

I teach my intro course using Anton's book as well, but Strang's lectures from 1999 are available via MIT OCW. These are good lectures if you are following in Strang's book, which is a good book with good exercises. I would not describe it as an easy book, though.

This is an interesting book as well: