/sqt/ Stupid Questions Thread

This thread is for questions that don't deserve their own thread.

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I'm at a community college right now. (It's actually a really good one for the science lower divisions).
I'm going for a BS in a biochemistry so I mapped out my course plan. I've never taken a physics course before and I will need a year of it when I transfer to uni. Should I take a baby physics course over a summer as a way to prepare for the relatively more difficult physics later on? Or would I be better off taking a math course as a way to boost my math skills? Would you guys recommend I take extra chemistry/biology classes to fill up my upper divisions or take on a minor in like computer science? Goal is to go to grad school btw.

I am absolutely torn between going into academia (math or statistics) or going into industry, making a lot more money and fucking with a relationship and shit.

Fuck

>Goal is to go to grad school
This is a question for your advisor then, do not take recommendations from internet strangers on a 6 year academic plan.
Physics is super math heavy so depending on your current skill level, it may behoove you to take some of it before taking physics. Only if you can jump straight into calculus though.

>I'm going for a BS in a biochemistry
Why are you fussed about physics/math then?
I mean, if you can afford it and want to sure. But I don't think anyone will really care about your physics grades.

>Would you guys recommend I take extra chemistry/biology classes to fill up my upper divisions or take on a minor in like computer science?

What do you want to do with your degree? For biochem, I'd probably fill up on extra chem/bio classes if you want to do something in science with it. If you dont, then yeah cs would be a good minor

Ask yourself what you want to do with your degree???? Then the answer should be clear

>Let A be a real n-by-n matrix. Show A is conjugate to a diagonal matrix only if there exists a basis of R^n consisting of eigenvectors
I'm not asking for a direct answer to this, but where the hell do I even start looking? I've only barely figured out how to show two different bases of the same Vector space are conjugate.

Think about how A acts on its eigenvectors and prove that they form a basis.

So if I understand eigenvalues correctly, they're effectively the scalars applied to vectors in V in the linear map T:V->V to yield v' or what-have-you, right?
So the only logical way for these to remain linearly independent (as a linear map) is for the eigenvalues themselves to form a basis of the vector space they're applying to?
Or am I missing a part/skipping ahead
I've only done computational stuff and nobody ever told me what the hell any of it meant

I have asked this in another thread with no answers.

What does it mean when the amount of equations and unknowns are the same? Does it make any difference if there would be one more unknown than equation? Does it mean that if the amount of unknowns is equal or less than the equations, then the unknowns are completely determinate? (that's what I'm thinking) Does this always hold true?

iirc Fewer unknown than equations (or the same) does not guarantee solvability, but more unknowns than equations does