# Can someone help with some linear algebra theory?

Asked by

nicky (

207)
October 19th, 2011

I am a computer science student at San Francisco State. This means I have to take a MILLION math classes.

I am on my second try at linear algebra and I thought I’d better ask anyone and everyone as many questions as I can.

We’re getting close to the half way point in the class and I believe I am suffering from not fully understanding the concept of Rn. I understand R2 is a two dimensional plane and R3 is a three dimensional plane etc., but is this different from a matrix with dimension 1 or 2?

I am a little fuzzy about transformations and how a subspace of R3 can be composed of vectors that ‘live’ in R2…

These are my preliminary questions and im looking for those helpful hints and tricks to help someone understand because the theorems for a lot of this stuff make sense, but at times they are too abstract for me to visualize for that ‘complete’ understanding.

Think of my understanding thus far as a slice of swiss cheese; it definitely exists, but full of holes :)

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## 5 Answers

R^n is the set of n-tuples of real numbers. A matrix is a rectangular array of real numbers; the size of a matrix is specified as nxm for integers m and n, where n is the number of rows and n the number of columns in the array. A linear transformation T is a function from R^m to R^n for some m and n with the property that for any vectors (m-tuples of real numbers) u and v, and any real numbers a and b, T(au+bv) = aT(u)+bT(v). Matrices and linear transformations correspond: any mxn matrix gives a linear transformation from R^m to R^n, and every linear transformation is represented by a matrix.

I’m going to stop here and leave you some advice. If you as lost as you claim at the halfway mark of a second try at linear algebra, seriously consider another major before you waste any more time and money. Linear algebra is trivial compared to the math you’ll need to master.

@ratboy, Thank you for your response… You do however have me on the defensive from your last comment.

To what math are you referring that i will ‘need’ to master?

@nicky asks: ”*I understand R2 is a two dimensional plane and R3 is a three dimensional plane etc., but is this different from a matrix with dimension 1 or 2?...I am a little fuzzy about transformations and how a subspace of R3 can be composed of vectors that ‘live’ in R2…*”

It’s been a *really* long time since I studied linear algebra but I think R3 is better described as a 3-dimensional space rather than plane (even though one can speak of higher-dimensional hyperplanes).

I agree with @ratboy that a matrix corresponds to a linear transformation.

Not sure what you mean by “vectors that ‘live’ in R2?” My understanding is that a 2-d plane embedded in 3-d space represents a subspace. (basis vectors & all that…) Besides the ever-reliable Wikipedia, another good online math resource is Wolfram MathWorld.

@prasad Wow, I used **Kreyszig** for 4 semesters 1968–1970 as a physics major! It’s still on my bookshelf – a beloved classic.

You may want to check out KhanAcademy.org or PatrickJMT.com for some great, well-explained video tutorials. Definitely helps give you a couple other perspectives when your book isn’t clear.

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