Relearning Matrices as Linear Functions
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Relearning Matrices as Linear Functions
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Re: Relearning Matrices as Linear Functions
#2FWIW, I was told that matrices are linear maps pretty early on in my education. Are there any college level linear algebra / matrix calculations courses that don't tell students about that?
Re: Relearning Matrices as Linear Functions
#3Who is "we" in this context?
Re: Relearning Matrices as Linear Functions
#4FWIW, I was told that matrices are linear maps pretty early on in my education. Are there any college level linear algebra / matrix calculations courses that don't tell students about that?
I agree. It's called Linear Algebra for a reason. :) That said, I still like the presentation given in this article.
Re: Relearning Matrices as Linear Functions
#5Who is "we" in this context?
me for example. My teachers in college did a real shit job at teaching this subject.
Re: Relearning Matrices as Linear Functions
#6If you're interested in this approach to linear algebra you should read Linear Algebra Done Right by Sheldon Axler.
Re: Relearning Matrices as Linear Functions
#7FWIW, I was told that matrices are linear maps pretty early on in my education. Are there any college level linear algebra / matrix calculations courses that don't tell students about that?
> FWIW, I was told that matrices are linear maps pretty early on in my education. Are there any college level linear algebra / matrix calculations courses that don't tell students about that?
I know they taught us about matrices in high school, but I don't recall them talking about any applications at all. I think the topic was pretty drained of context, just rote application of the rules for add/subtract/multiply/etc.
Re: Relearning Matrices as Linear Functions
#8FWIW, I was told that matrices are linear maps pretty early on in my education. Are there any college level linear algebra / matrix calculations courses that don't tell students about that?
It's possible if you learned matrices outside the context of a linear algebra class that you might be mystified about what's actually happening.
I took Linear Algebra the same semester I took Computer Graphics, which worked out really well for me - the first half of LA taught me everything I needed to know about transformation matrices, and the second half of CG covered 3D graphics in OpenGL. The first half of CG was all 2D graphics stuff, and the second half of LA was about eigenvectors/values - I've forgotten everything from that part of the class.
Re: Relearning Matrices as Linear Functions
#9If you're interested in this approach to linear algebra you should read Linear Algebra Done Right by Sheldon Axler.
Or pretty much any other Linear Algebra book.
Re: Relearning Matrices as Linear Functions
#10Good, intuitive introduction to matrices. Next steps could be showing that there are infinitely many different matrix representations of a linear map (different from the polynomials) and they can be used for function spaces, too.
One question that usually pops up that I was confused about till recently: are rank two tensor equivalent to matrices? Answer is no, e.g. see here: https://physics.stackexchange.com/questions/20437/are-matric...