/sci/ - Science & Math

[Anonymous No.10518712]

who noticed first that functions and vectors have similarities ?

[Anonymous No.10518715]

>>10518712
what's the similarity? the brackets?

[Anonymous No.10518716]

>>10518715

retard

[Anonymous No.10518717]

>>10518712
There's no similarity

[Anonymous No.10518739]

>>10518717

then why can I project a function on another function to get an approximation just like vectors?

[Anonymous No.10518756]

>>10518739
you can project a frog on a wall, doesn't mean they are similar things

[Anonymous No.10518951]

>>10518712
i’m gonna go with Fourier.

[Anonymous No.10519337]

>>10518951
I'm guessing it was earlier than that. For analytic functions their Maclaurin series can be used to expand in terms of the x^n bases, which were discovered ~50 years prior

[Anonymous No.10519342]

>>10518739
If your function lives in a (pre-)Hilbert space, then yes, you most certainly can project it into another function. That's the whole point.

[Anonymous No.10519352]

>>10518712
You might find this article about the history of functional analysis interesting: http://courses.mai.liu.se/GU/TATM85/FA-history.pdf

[Anonymous No.10519357]

To break this down, it will help if you first strip the algebraic features of a vector and few the enumerated array aspect of it: Arrays are functions with a finite index set as domain.

If the values of the functions/arrays are elements of an algebra, then the functions/arrays inherits it.
E.g. if you look at functions/arrays taking values/components in the reals, then you can pull that back and define an algebraic relation on the functions/arrays. That makes either of the two into e.g. vector spaces.

[Anonymous No.10519365]

>>10519357
>if you first strip the algebraic features of a vector
That's the only features a vector has. There is no "enumerated array aspect" of vectors