|
|
|
|
|
|
by ttoinou
340 days ago
|
|
|
The article : You may recall that this representation is only one example of an abstract vector space. There are many other types of vectors, such as lists of complex numbers, graph cycles, and even magic squares.
However, all of these vector spaces have one thing in common: a finite number of dimensions. That is, each kind of vector can be represented as a collection of N N numbers, though the definition of “number” varies.
So the goal is to impress the reader by letting him believe we will easily apply our easy linear algebra to real -> real functions. But we can't. |
|
|
When you only have a finite number of functions (and the space they span), then you can apply your finite dimensional linear algebra, since n dimensional vector spaces over a field are isomorphic. You absolutely can gain intuition for real functions from arrows on a paper type vectors.
E.g. the article mentions the Cauchy-Schwartz inequalities for functions, that's something you can intuit when you imagine our functions being little arrows on a paper.