@NovaliumCompany Watch 3Blue1Brown and Khan Academy

@EmilioPisanty Sure, everything is to be taken modulo future events

@NovaliumCompany I saw a neat example about that a couple days ago with RGB color space. Your basis vectors are $R$, $G$, and $B$. You can have linear combinations such as $\frac{1}{2}R + \frac{1}{2}B$ that comes out to be purple in that specific case. The span of those bases is the entire RGB space. You could also come up with something like $\textrm{span}(R, B)$ that would cover red, blue, purple, and all between.

Ok, 3Blue1Brown seem nice, I think I'll be fine. If I really don't understand something and I've tried hard to understand it, I will ask :)

Or I suppose if you wanted to change basis, you could go to CMYK space

@Blue mathematica output:

@danielunderwood Unfortunately, color gamuts are actually more complicated than that :P

Aw man. I thought it was a neat example. I don't know too much about colors though

 {{0.157747 + 0.522448 I, -0.657747 - 0.0224476 I, -0.304193 - 0.168894 I, 0.195807 + 0.331106 I},
  {-0.657747 - 0.0224476 I, 0.157747 + 0.522448 I, -0.195807 - 0.331106 I,   0.304193 + 0.168894 I},
  {-0.304193 - 0.168894 I, -0.195807 - 0.331106 I, 0.157747 + 0.522448 I,   0.657747 + 0.0224476 I},
  {0.195807 + 0.331106 I, 0.304193 + 0.168894 I, 0.657747 + 0.0224476 I, 0.157747 + 0.522448 I}}

there we go

There are several RGB color models that map differently onto "true" color space, and it doesn't really behave as a vector space - consider what happens when you add an RGB value to itself vs. what happens when you add a vector to itself.

(The vector doubles, and it's not really clear what happens to the color, but the straightforward result of adding a color to itself is just the same color)

yeah, checks out for me

np

@ACuriousMind Couldn't you just choose a different definition of addition? Like a vector space doesn't put any restriction on addition as long as it's defined, right?

@danielunderwood But $v + v = 2v$ is a consequence of the axioms.

my advice would be to look at some examples of code

nothing sophisticated

In fact, it's not addition that's the problem, but I can't really tell what scalar multiplication is supposed to be for RGB colors

sigh

I can never to get it to offset like code when I want it to

You could cut out some of that, though: for instance, you could just do

MatrixExp[I*2*Pi/16*1/4*{{15, 9, 5, -3}, {9, 15, 3, -5}, {5, 3, 15, -9}, {-3, -5, -9, 15}}]//FullSimplify

yeah, I think the issue was that my first line wasn't code and I wasn't offsetting it

so apparently it's an all-or-nothing format

if you want numerical output, you can do //N at the end

(that's basically a short-hand for N[stuff])

i.e. g//f is the same as f[g]

which is convenient if you just want to do a quick command without worrying about braces etc

not useful for a command with multiple arguments, though

there's a few other notational things like that

mostly for pattern-matching purposes

@ACuriousMind could you define a space where any scalar multiplication is identified with kind of a "fundamental"? So $n(R+B) = R+B$ and similar. I don't know that that's technically a vector space anymore. And I suppose if you had $n < 1$, you can't do that identification anymore. BTW is there a mathematical object that's somewhat like a vector space, but there's an identification like this?

Really $n$ would have to be a natural number in that case

And any scalar multiplication would need a whole number subtracted until you ended up with something in $[0,1]$

@Semiclassical a//f[#,b]&

nice

yeah, that'd work

but at that point I feel like it's easier to just do f[a,b]. (depends on the situation, of course)

I believe you've killed that analogy. Though it seems like it would be some sort of mathematical object

@Blue it depends on how much time you have to devote to it, but if you have any sizeable stretch then I strongly recommend this course

can i ask a dumb sci fi question

Guys, I took a quick look at MOSFET transistors and they seem to act just like the BJT, is there even any difference?

@ACuriousMind was this user suspended just to keep their total vote count pretty for longer?

@Blue Thanks :-D

@EmilioPisanty That link doesn't go where you want it to go, but rest assured aesthetics rarely enters into our decision process :P

@ACuriousMind it goes exactly where I want it to go

thank you very much

;-)

@Blue In a BJT will the current from base combine with the collector at the emitter?

Heh

oooohhh, also

I should vote 30 more times and then stop forever

@Blue So I can use a transistor as an amplifier by putting a small audio signal (for example) through the base and large current through the collector, and the transistor will spit an amplified version of the audio signal?

they should give this guy a lurker badge

eleventh place on all-time votes

zero questions, zero answers

just ~forty rep from suggested edits

@Blue Ok thanks. See you :)

Ugh...not looking forward to the new site themes