Can someone red pill me on linear independence? I see it in my

>>8640664
What the fuck do you need a red pill for?

A set of vectors is independent if none of them can be written as a linear combination of the others.

A set of vectors is dependent if at least one (all) of them can be written as a linear combination of the others.

That's it. Here's your PhD in linear algebra. Congratulations.

>>8640685

I was more so getting at the implications of that.

>>8640664
Who are those two?

Can anyone give me a quick rundown?

>>8640696
please no

>>8640664
Can someone redpill me on addition? I learned it in kindergarten obviously but now it's popping up in my advanced topological shitposting II course...

>>8640696
kys

>>8640690
If something is linearly independent from some other stuff then it basically represents another layer of complexity to what you can make by combining all those things.

So say you've got a bunch of vectors that all only point along one line, maybe forwards or backwards, with those you can only every describe points on a line (by adding and multiplying them). As soon as you get a vector that points in even slightly a different direction (i.e. forms an angle that isn't 0 or 180deg with the others) you can now use it with the others to describe points in some 2D plane. The new vector is linearly independent from the others because there is no way to represent it by combining the old ones, whereas the old set can all be represented by combinations of each other because they're all on the same line.

>>8640664
>Where else does this fucking thing leech to?

absolutely fucking everywhere

File: bog-vatican.jpg (2MB, 3072x2184px) Image search: [Google]

2MB, 3072x2184px

>>8640696

>>8640696
>>>/a/nywhereelsebuthere

>>8640664
Who are these guys? Can someone give me a fast walkup?