Can someone help with some linear algebra theory?

Practical algebra lessons

I didn’t get what Rn is. If it’s vector, you may read basic vector operations here. If you want to go up to differentiation and integration, you may look in Kreyszig. I don’t know about Kreyszig, but many students refer it. I got almost everything on scalars and vectors from Vector Mechancis for engineers by Beer and Johnston; it is a mechanical engineering book.

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.