Matrix tips

>>7810343
practice more
there's no magic to doing them faster in general any more than there is magic to adding general numbers fast. You're just uncomfortable with the machinery.

also
>reducing matrices by hand
>ever
nice lin alg for engineers course

>>7810343
>doing them by hand
m8 if you reduce more than like 10 matrices in your entire life you're doing it wrong.

It's ok to do it a bunch of times to understand the technique but then either use matlab/numpy or write your own program.

>>7810343
Easy. Skip immediately to the proof-based problems.

Gauss-Jordan is really easy, you just need to practice. It's really worth it. Once you can do it in your head, you can do all kinds of interesting manipulations when you're trying to figure out problems without having to do it on paper.

I work in computer graphics, so I need to work with a lot of 4x4 transformation matrices, and I need to do this kind of thing when I'm working between cameras and screen spaces, so it's a valuable skill to have for me.

If you don't know why you're learning this yet, just trust your professor. Standard linear algebra courses are usually meant to be entirely practical. Ive never seen a textbook that focuses on the theory behind it (but I'm dying to find one).

I won't be able to use a calculator on any of the tests, last alone matlab.

If you're going for something like rref, start in the bottom left and use elementary operations to create 0 after using some flipping and go from there. Apparently I'm the only actual mathematician here and not some wannabe engineer bitch.

>>7810702
>. Ive never seen a textbook that focuses on the theory behind it (but I'm dying to find one).
There are plenty, e.g. Axler, Shilov, Hoffman/Kunze.

>>7810702

We used Axler's in my intro linear course. Granted, a lot of people in the class weren't very bright and we didn't get through much of the book. It was nice learning the theory before learning the plug n' chug matrix techniques, though

G A U S S
A
U
S
S

J O R D A N
O
R
D
A
N

>>7810728
If your professor is going to ask you to compute matrices in a test then you are going to a shit school.

I mean, one or two computations with simple numbers so that it is only to show that you understand the algorithm is fine but you make it sound like the test will have you spend a significant amount of time doing computations.

Such a shame. There are so many baby tier proofs in linear algebra that your professor could put in the test instead.

>>7811023
Still takes for fucking ever


It's 2016 for fucks sake. Some dick weed figured this shit out centuries ago and we still can't figure out how to do it faster

LU Decomposition.

>>7811062
What the hell are you talking about? GJ is O(n^3), and in 1990 Coppersmith–Winograd algorithm was made that is O(n^2.375477), then in 2010 it was improved to O(n^2.374).

>>7810343
Tell your professor to use Z/pZ instead of R to simplify the arithmetic