# Is a full semester of Linear Algebra really needed if I want to specialize in computer graphics?

I'm a graduate student in computer science and would like to specialize in computer graphics, but I have never taken a full semester of Linear Algebra. I have, however, taken calculus I - IV, and differential equations. I picked up matrix multiplication and vector math in my physics classes.

During my first semester of graduate school, I took Intro to Computer Graphics and told the teacher of my situation. He said it's fine if I take the class but if I want to specialize in computer graphics I will need to eventually take linear algebra.

I could just take his advice and be done with it, but I didn't struggle in any way with the matrix/vector math we needed for the Intro to CG class.

Is there something that I'm missing? Do I really need to pick up linear algebra if I want to pursue computer graphics seriously?

Is there something more advanced than matrix multiplication or quaternions that you need to know in order to do computer graphics?

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Well, if I were ever to give an unsolicited advice to anyone, I'd suggest sit through the linear algebra class throughout the semester whether or not it is immediately clear how it will be useful to your research. – Dilawar Feb 28 '13 at 16:26
I don't understand how you managed to take multivariable calculus and differential equations, but no linear algebra. What was your undergrad?? – Math1000 Apr 6 '15 at 23:28

You're not likely to need much more than matrix multiplication and quaternions to get by, but as Qiaochu said, the stronger your Linear Algebra background the better-off you'll be; in computer graphics particularly it's the discipline you'll use more than any other advanced mathematics, by far. Do you know how to determine the change of volume for a given linear transformation? Do you know how normal vectors are different from position vectors, and do you know why? Do you know what the adjoint to a transformation (matrix) is, how you might compute it, and why you might need to? Do you know what's meant by the statements that the quaternions are a double cover of the rotation group, and do you know the practical consequences of that statement? (Here's one particularly fascinating and unusual consequence)

If you're not immediately familiar with all of these, I'd heartily recommend taking the Linear Algebra class. (And if you are immediately familiar with all of these, then you should seriously consider talking to your advisor about whether it's possible to test out of Linear Algebra, because you should have a strong enough foundation to make that feasible.)

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Ok, I don't know any of this stuff so I better take a full semester. – Joey Green Apr 8 '11 at 23:27

Linear algebra is useful for almost any applied subject. There's no reason not to learn as much of it as possible, and expect to find more applications of it in computer graphics the more you learn about it.

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You should be very clear on basis changes, for instance. A full semester of Linear Algebra is not really that demanding and is certainly good for you. BTW, have a look at this book: http://www.farinhansford.com/books/pla/

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We did basis changing in the Intro CG class. It was probably the toughest subject of the class for me though. – Joey Green Apr 8 '11 at 19:25
That book also looks great for me. – Joey Green Apr 8 '11 at 19:28
@Joey, if you found basis changing hard, you should take Linear Algebra. – lhf Apr 8 '11 at 20:50
quite correct! – Mariano Suárez-Alvarez Apr 8 '11 at 21:58

If program requirements, or your supervisor, demand Linear Algebra, the answer is clear.

But if not, then I think that a semester of Linear Algebra may not be a high priority item. You have some mathematical background, and can pick up things as needed. Also, Linear Algebra courses are typically, and unfortunately, often weak on making connections with geometry.

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You must have had the wrong LA courses; the geometric connections were often the primary motivating examples in the handful that I took. – Steven Stadnicki Apr 8 '11 at 21:15