Where is /sqt/?

Stupid questions thread then.

Can someone help me understand why matrices are so great?
What am I missing here?

Other urls found in this thread:

benfrederickson.com/matrix-factorization/
acko.net/tv/webglmath/
youtube.com/watch?v=sZ2qulI6GEk#t=60
proofwiki.org/wiki/Order_of_Element_Divides_Order_of_Finite_Group
proofwiki.org/wiki/Lagrange's_Theorem_(Group_Theory)
twitter.com/SFWRedditImages

benfrederickson.com/matrix-factorization/

(i haven't actually read that image, but here's some cool applications of matrices)

I can't fucking study

I always
open Veeky Forums
open social media
open porn
open youtube


FUCK

Go study somewhere without a computer then

Best thing?
Solving large systems of equations

For example, a truss in static equilibrium generates 3 equations for each member and a common problem (in class) would have something like 7-8 members.
So you end up with 21-24 equations you need to solve for to get forces and thus stress.

Plugging it into a matrix makes it algorithmic, instead of solving for each unknown individually by plugging and manipulating algebra.

Except I need my computer to study. What I need and I don't have is self-control and self-discipline

>people never studied before computers

learn how to do calculations by hand and find books in the library by walking around you fucking degenerate moron. you really think von neumann needed a fucking macbook to design eniac? no he just had to get a carbon copy turing's. no macbook necessary.

Any linear map between finite dimensional vector spaces can be completely determined by a list of numbers, from which we can glean lots of information about eigenvalues, injectivity, etc. very easily. I'd say that's pretty great.

>20-something
>large

Try millions or tens of millions in harmonic analysis of a structure like a rocket

Essentially this. When you can reduce the study of a complex object (linear maps between finite dimensional vector spaces) to some numbers, you can say it's a great success in math. In addition:
> a particularly interesting case of this are base changes (where the matrix is invertible)
> this includes geometric manipulations (f.e. rotations)
> apart from all of this, programs run a lot faster when they do their operations in matrices instead of 1 by 1.

What happened between these two steps?

I can see how matrices would be useful in engineering and that.
But the specific example of matrices I want to know about it the matrices used by graphics processing units. GPUs are specifically designed to accept and operate on matrices because apparently it's faster? But I can't see how, hence the OP picture.

Distributive property?

They just collected the terms

What does it mean for a matrix to be positive semidefinite?

If M is your matrix, [math] |x \rangle [/math] any vector and [math] \langle x | [/math] its covariant representative, then
[math] \langle x | M |x \rangle \geq 0 [/math]

Why haven't we talked about exotic particles yachting negative mass imaginary mass God particle

Its just an example dude.
GPUs use matrices for intense lighting calculations.
I haven't implemented them myself, but I remember reading something about orienting vectors (like that object is at 0,0,2 from the player) via matrix multiplication
You can use them for any system of finite linear equations.

To find the equation of the line that best "fits" a bunch of data points (minimises MSE for instance) -- do you always have to do the thing with linear regression? Is there no closed form formula that just gives me the coefficients?

Not him but for many of my classes the homework and all that is done online through some portal so you're required to have a computer

We use matrices to plot tensors in stress analysis

Recently I was trying to find the expected value of a matrix with restricted row and column sums. The method I devised involves solving for the hypervolume of an (m-1)(n-1) dimensional polytope, which involves solving a large amount of nested integrals. Is there an easier way to do this?

>highschool

What contents should I know before Calculus?

go study first.
let's talk again in 3 years.

Matrices just map from one vector to another, without leaving the corresponding vectors space. This can then be specialized to a great many things in any field of science, even the shitty soft ones.

>Except I need my computer to study
Why?

Functions, sets, polynomials

I have a 17 year old nephew who doesn't care about high school and just created a twitch account where he thinks he's gonna be rich. The kid has five Fs this semester and he averages 3 failed classes per semester since 9th grade. My nephew will be 18 in February. What is there to do with him?

it will suck in the short term (only a few years, if you're lucky) but you probably just have to let him have his journey and figure it out
if he can't figure it out on his own then there is no hope and nothing to be done, so don't worry about it at that point
if he can figure it out on his own then it will be all the sweeter and more beneficial for the rest of his life

and by figure it out on his own i mean realize that there's more to life than video games and he's likely just wasting his prime years away, and that he should probably do more with his years.

notice all the probablys and maybes? Maybe this is his path. Whatever. He'll figure it out. Or he won't. Either way is something he has to do - not something you can force.

So I have been told that, if f is derivable in x, [math]\lim_{h\to 0} \frac{f(x+h)}{h}-f'(x)=0[/math], but I can't figure out how to prove it. How do I do it, Veeky Forums?

It's a shit reality but the other user is right. If you think you have a shot in hell of trying to tell a teenager what to do, you've forgotten what it's like to be a teenager.

If he wants to fuck his life up you can't stop him. Best you can do is be available to help if/when he decides to fix it.

okay, you scaled the cube which is orthogonal to all the axes of your space. Now try turning it.

The first term is the definition of the derivative of f at x. The second term is the derivative of f at x. You're literally subtracting two things that are by definition the same (assuming, as here, that f'(x) exists).

Wait, sorry, as you wrote it, it doesn't work at all. Let f(x) = x. f'(x) = 1, so it exists. But the limit is (x+h)/h as h->0, which is undefined. So the statement is false.

It's the limit of the whole expression, [math]\lim_{h\to 0} [\frac{f(x+h)}{h} - f'(x)][/math].
Does it make sense like that?

Doesn't matter, the f'(x) is independent of h, so it pops out of the limit. The first term should be [f(x+h)-f(x)]/h as h->0 to make the expression a valid equation.

You are right, turns out the person who told me skipped the-f(x) by mistake.
Thank you.

I have an overkill PC that doesn't hit 30% no matter what I do. Any programs that can take advantage of the processing power whilst teaching me a thing or two? Like protein structure simulation or something to that effect (for free)?

How do I show [math] \langle \mathbb{R}, + \rangle [/math] is isomorphic to [math] \langle \mathbb{R}^{+}, \cdot \rangle [/math] with [math] \phi : \mathbb{R} \to \mathbb{R}^{+}[/math] defined by [math]\phi(x) = 2^{x}[/math]? I know i have to show one-to-one, onto and [math] \phi(a + b) = \phi(a) \cdot \phi(b) [/math]. I just don't know how i would show these things. (first abstract algebra class, if that matters)

Has anyone used Engineering Mechanics by RC Hibbeler? Is it good?

>I know i have to show one-to-one, onto
The explicit inverse is incredibly easy to state.

acko.net/tv/webglmath/

To show one to one, you need to show EITHER:

f(a) = f(b) implies a = b

OR

a != b implies f(a) != f(b)

This is easy, though.
Suppose f(a) = f(b).
Then, 2^a = 2^b.
Take the log_2 of both sides.
That tells you a = b. Right? If two powers of 2 are equal, then their exponents need to be the same.

To show onto?

You need to show that any element in R+ is mapped to by some element of R by your map. So, take b in R+. If you want b = 2^x, what element of R maps to it? Well, I think it is log_2(b). Notice that this is OK because everything in R+ is positive.

Pretty good, but if you like theory should complement with some other books like Beer that you can find easily

so for onto, it would be: Let [math] b = 2^{x}, b \in \mathbb{R}^{+} [/math]. Since [math]\log_{2} b \in \mathbb{R}[/math], [math]\mathbb{R}[/math] and [math]\mathbb{R}^{+}[/math] are onto.

??

OP's picture:

> Guns are terrible compared to spoons as a tool to eat yogurt. Guns are therefore a terrible weapon.

Dude...

Hey guys, here.

I'm planning on modeling atom representations for all (or the most I can) elements based on the Schrodinger's equation. I've come across a few, mainly the hydrogen one, but for the heavier elements I haven't had much luck. They seem fairly easy to design 3D-wise, and I want to do molecules at some point too if possible, so I was hoping if I could get some input from you guys since my knowledge of chemistry and quantum physics isn't that extensive.

>To show one to one, you need to show EITHER:
>
>f(a) = f(b) implies a = b
>
>OR
>
>a != b implies f(a) != f(b)
They're groups -- he just needs to show that only 0 maps to 1.

For multi-electron atoms you need to solve the Schrodinger equation numerically, I'm not very well versed in molecular modeling, but Google it and you'll find some better references then I could give you.

>ivy league university

In the OP:
How are you forming your matrix?
How are you multiplying your matrices?

You want to scale a cube, a shape in R3, but in your matrix, you have 4, 6 dimensional vectors, or 4 6-tuples. Then, when multiplying them, you have a 4x6 matrix multiplied by a 4x4 matrix.

I understand that 3*8=4*6, but you can't just shift around the number of components in each vector. Moreover, when scaling a matrix, we don't multiple by the scalar times the identity matrix, we just multiply our original matrix by a scalar.

If you want to learn why matrices are so great, go read up on them first. Grab a linear algebra book and start working through it. It's well worth your time.

If this is a troll, however, well done. 10/10, you got me.

or is it: Let [math]a \in \mathbb{R}, b \in \mathbb{R}^{+}[/math]. Suppose [math]\phi(a) = b[/math]. So [math]2^{a} = b[/math], [math]\log 2^{a} = \log b[/math], [math]a \log 2 = \log b[/math], [math]a = \frac{\log b}{\log 2}[/math]. So [math]a[/math] maps to [math]\frac{\log b}{\log 2}[/math]. Thus, they are onto. [math]\blacksquare[/math] ... ?

Are you me?

Wait, so all those shapes from the pic I posted correspond to the hydrogen atom? I don't get it, how does the electron cloud vary so wildly with just 1 electron? Forgive my ignorance, user.

>How are you forming your matrix?
>How are you multiplying your matrices?

The matrix is formed by lining up the eight vertices vertically.
The vertices have 3 dimensions plus the homogeneous coordinate, so 4 dimensions total. It is actually 8 4-tuples

Again, I specifically wanted to know why matrices are good for graphics processing, hence taking into consideration the homogeneous value plus forming the matrix like a graphics processor would.

I should have used values other than 1 and -1 to make it more clear

>lying

Spherical harmonics are a hell of a thing.

For computer graphics, many operations to produce images are just vector arithmetic, scaling, skewing, reflecting, etc... Can all be handled by simple mathematical operations on points to find new transformed points.

So you end up with a system of linear equations to solve, and matrix algebra gives you a really easy and computationally efficient way to solve them.

Since I'm here. I'll ask this. Being Veeky Forums I might not be crowned immortal emperor of autism.

I want to track some life-success metrics in order to motivate and monitor myself through an irregular polygon. You might have seen it in fighting games, or similar places.

The final result would be an irregular polygon. Besides the distance to the vertices ('score' of each particular metric), I'd like to calculate the area, as some sort of general 'score' of how well I'm doing.

I'm not looking for advice in how to implement it, but about how to assign the 'stats' or 'skills' to each vertex so the area ('score') reflects something meaningful.

i.e. Assign stats that have low or zero synergy aligned and those that complement well with each other forming an angle close to 90ยบ.

Chances are I haven't explained myself very well, but if you could help me out, I'd appreciate it. Ask for clarification if I'm not making much sense.

Is the Laplace operator a functional?

What else could be added for carbon fibers for different effects? I know the carbon fibers on a plane have an oxidize surface, with an epoxy layer. But carbon fibers are composites, so what else would be added?

Is it a secret?

Nope, since it maps one function onto another, not unto a scalar

When convoluting a harmonic signal with a finite impulse response, do I take harmonic represented by a frequency of 1*fundf as corresponding with the unit impulse of [eqn]\delta[n][/eqn]?

see 13:00

youtube.com/watch?v=sZ2qulI6GEk#t=60

I'm sorry I can't understand your question.
Can you elaborate? It seems some notions are lost in translation

Any good starting materials on wavelets?

The following was a question for an abstract algebra exam. I have no idea how to solve it, wondering if anyone knows how to prove it:

Let [math]\langle G, * \rangle[/math] be a group, and for any elements [math]a, b, c \in G[/math], show that the equation [math]a * x * b = c * a[/math] has a unique solution, and find such solution.

Matrices are fantastic.
They can simplify systems of differential equations, they can let you take derivatives without actually taking derivatives, they let you do complicated transforms easily, etc.
Basically, if you can find an isomorphism between the set you're working in and a set of matrices, you can simplify many problems into a set of matrix operations.

suppose [math]a*x*b=c*a[/math] has two solutions for [math]x[/math], [math]e[/math] and [math]f[/math]

substituting we see [math]a*e*b=a*f*b[/math], using left and right cancellation laws, [math]e=f[/math]

the solution is [math]a^{-1}*c*a*b^{-1}[/math]

alright, for people who know combinatorics:

i want to tile a 2xn set of spaces with tiles, which are 2x1 and 1x2 in size.

now, our a0 terms and a1 terms both cannot be tiled. does that mean a0=0 and a1=0?

oops, i mistyped the problem.

the spaces are 1xn, and our tiles are 1x2 and 1x3. just wondering what the a0 and a1 terms are.

i thought the solution was suppose to be what the binary operation actually was, so it should be manipulated like this:
[math]\begin{align*}a * x * b &= c * a \\ a^{-1} * a * x * b &= a^{-1} * c * a \\ x * b & = a^{-1} * c * a \\ x * b * b^{-1} & = a^{-1} * c * a * b^{-1} \\ x &= a^{-1} * c * a * b^{-1} \end{align*}[/math]

that's basically how i calculated the solution, showing uniqueness requires using the theorem regarding left and right cancellation

im pretty sure she assumes we can prove cancellation law anyway, so i could probably just put by cancellation law and thatd be enough. thanks

[math] \text { prop } [/math] Let [math] A [/math] be bounded above such that [math] s = Sup ( A) [/math] exists. Then [math] s \in \bar { A } [/math].

[math] \text { Proof } [/math] If [math] s \in A [/math] then there is nothing to prove, so suppose that [math] s \not \in A [/math] then let [math] \left ( x_n \right ) [/math] be a sequence in [math] A [/math] then [math] Sup ( A ) - 1/n \leq x_n \leq Sup ( A ) [/math] which means [math] \left ( x_n \right ) \to s = Sup ( A ) [/math] and so [math] s \in \bar { A } ~ ~ \blacksquare [/math]

I think this is okay, but I'm not sure, anyone got any constructive feedback?

s can be in A though..

he already dealt with that case

try to separate the cases and don't say things like "there is nothing to prove", it doesn't sound very good. Just say if "s in A, then s in bar(A) since A included in bar(A)"

now for the other case, you say nothing about your sequence xn.

Am I supposed to trust that any sequence of elements in A gets infinitely close to sup(A)? That sounds strange... (and it's false of course, so maybe you forget something)

try to define x_n as precisely as possible.
For example, x_n = s-1/n. Or at least something like "there exists at least one real number between s-1/n and s, choose x_n in that interval".

By the way, is A an interval? Because that previous statement is not trivial otherwise...
For example, if A is the intersection of R\Q and [0,1[ (0 included, 1 excluded), it can be a bit harder.

Try to think of all the doubts you could have while reading your proof. If you want more feedback, try rewriting it now, it will probably be much better already!

>he already dealt with that case
if [math]s \in A[/math] his proposition is wrong. There are sets such that [math]s = \sup A[/math], and [math]s \in A[/math]. [math] \bar A[/math] is the compliment of [math]A[/math], not the set of upper bounds of [math]A[/math]. The way his proposition is now, it does make any sense.

*doesn't make any sense

Use \sup for [math] \sup [/math]

Is [math] \bar{A} [/math] the closure of A?

In some situations, [math]\bar{A}[/math] denotes the closure of [math]A[/math]. Pic related, it is page 35 of baby Rudin.

A bar is the close of A in topology user

Now I understand why it looks confusing

how can i prove that if [math]\langle G, * \rangle[/math] is a finite group, for any [math]a \in G, \exists n \in \mathbb{Z}^{+}, s.t. a^{n} = e[/math] ??

my bad.

Look at the subgroup generated by a.

There's a few theorems that make this a one liner, but I'm going to avoid those. I'll just give you the idea. Let [math]a \in G[/math]. Then [math]a^2 \in G[/math]. Is [math]a^2 = e[/math]? If yes, then it's over, but if not, then look at [math]a^3[/math], and repeat. You will eventually reach the identity element.

Can anyone identify how I'm supposed to turn [math]1/(x+1)^2[/math] into series notation?

What's wrong with Taylor series?

i wrote this on the exam and it was marked 2 points off.. is there a principle/theorem of finite groups she might have wanted mentioned in the proof to give full credit? she is usually pretty lenient with grading so i dont know why itd be wrong

i just ended up using a modified geometric series

so would saying something like:
If [math]\langle a \rangle \neq G[/math], and [math]a \in G[/math], then [math]\langle a \rangle = H[/math], which is a subgroup of [math]G[/math], and contains [math]e[/math] by the definition of a cyclic subgroup.
be a good proof? or do i have to bring up that its finite at some point

>You will eventually reach the identity element.
This is really the part of the argument that needs justification.

Suppose there was no n such that a^n = e.
Then, < G, G must be infinite.

proofwiki.org/wiki/Order_of_Element_Divides_Order_of_Finite_Group
proofwiki.org/wiki/Lagrange's_Theorem_(Group_Theory)

is it even true?

what if G is the set of all exp(i*k*pi/m), with k and m being some integers? you can always use n=2*m

print it off, do it then input the answers after

fuck

i think because its finitie its true
so would saying, since [math]G[/math] is finite, then it has a generator [math]\langle a \rangle[/math] such that... i just dont see any theorem in the book that doesn't specifically say cyclic group. or am i missing one that says every finite group is cyclic?

Multiplication by a gives a homomorphism from the subgroup generated by a to itself. Since G is finite, it is not injective. Thus the kernel is nontrivial, and you're done.

Computing your results using a polygon is over-complicating what you're trying to do. You have a bunch of stats and you want "good" to be represented as further away from the center, so your shape gets bigger, thus more area. Instead of that, you might as well just add all the stats together.

Financial = 6.5
Autism = 5.2
Social = 2.1
Polybius = 6.6
Side projects = 3.5

Total score = 23.9

(e, a, b, ab) is clearly not cyclic but finite.
(Z/nZ) X (Z/mZ) is cyclic iff m and n are relatively prime for positive m and n.