Linear algebra struggle

[mathsdespair]

Hi everyone.
Long time lurker first time poster.
I am taking a linear algebra class this semester and I am really struggling.
Does anyone have any good resources for learning/understanding function spaces, polynomial interpolation and orthogonal expansion etc..?
Thanks

 

[Simon Bridge]

Welcome to PF;
Get a tutor.

There is a whole section on recommended textbooks and resources - the trouble is that we don't know you well enough to figure out what will work well for you and everyone is different.

A better approach will be to post some questions about your homework here and let us guide you through them - then you can learn how to handle them. It is still quicker to get a tutor.

 

[mathsdespair]

Ok thanks. Part of the problem is I do not know how to revise it. I did really well in analysis and I learned it by proving theorems, should I apply the same technique to linear?

 

[Simon Bridge]

I don't know. It's not an approach I'd use but you may learn things differently to me.
I see algebra as the grammar and syntax of mathematics - you practice putting sentences together.
The idea is to tease out relationships which may not be obvious ... so I'd concentrate on the relationships and the applications. OTOH I did not do well in algebra until my physics caught up and that's common with students.

Usually proving theorems can work well when your trouble is that you don't trust the foundations the later mathematical arguments are built on - you have trouble seeing how one part links with the others.

I still think that post #2 has the best advise for you going forward.

 

[Inner_Peace]

Does anyone have any good resources for learning/understanding function spaces, polynomial interpolation and orthogonal expansion etc..?
Thanks

You might like taking a look at Khan Academy's video tutorials on the Linear Algebra course. They are helping me understand a lot many things :)

 

[mathwonk]

your list of desired topics makes me think you want to know about vector spaces and linear maps in the presence of an inner product. this is a somewhat specialized topic within linear algebra, but quite standard. a good source might be mike artin's algebra book, or maybe shilov's book linear algebra, (shilov is very good and very cheap).\\

https://www.amazon.com/dp/048663518X/?tag=pfamazon01-20

i have a lot of free linear algebra books on my web page

http://www.math.uga.edu/~roy/

but i tend to somewhat ignore those subtopics of spaces with inner products. you may want to learn the method of "gram schmidt".