Difficult Linear Algebra Questions

>>8077500
Prove the existence or non existence of a magic square in dimension PxP where P is any prime number > 3 such all the numbers of the matrix are prime (and unique) and so that the sum of every row, column and diagonal is also a prime.

After that you get your PhD in linear algebra and number theory or something like that.

The main character is given some coordinates, he goes to that place but finds nothing. He gives up.
Plot twist: he finds some numbers.. turns out it is a matrix for changing the basis.. he does the fucking transformation, gets the new coordinates, goes to the actual location, finds XXXXX and wins.

BOOM

>>8077515
It's basically an interrogation scene, where the main character is interrogating a spy. After asking him a few easy questions, he gives him this really difficult problem full of words and terms specific to linear algebra like null space and transformation and eigenvalue--something along those lines.

>>8077500
Is this script in python?

>>8077525
open H&K or axler, go to the chapter on jordan canonical form and grab an exercise that sounds cool

popsci is always shit though, I hope you fail

Does it have to be solvable? Also why does it have to be from linear algebra?

>>8077675
>open H&K or axler, go to the chapter on jordan canonical form and grab an exercise that sounds cool
>JCF
>difficult

>>8077738
The spy has a Ph.D. in Gram-Schmidt orthonormalization.

File: 1463213258918.jpg (10KB, 267x200px) Image search: [Google]

10KB, 267x200px

>>8077777
>Ph.D. in Gram-Schmidt orthonormalization

>>8077777
You serious though?

>>8077744
Well grasping the subject is at first quite hard if you don't know shit about blocks and null matrices

File: 0dbb705287eeec6d33a00d5148847290.jpg (19KB, 236x314px) Image search: [Google]

19KB, 236x314px

Procrustes Method.

Align a buncha points onto another buncha points with rigid body (mmm) transformations and rotations.

Name based on Greek myth Procrustes, a bandit that made travelers stay at his house and cut them to size for his (always ill fitting) beds. You can work the myth into the script for some interesting lore.

The method itself is an SVD factorization of a matrix with the middle thrown out. Really simple/complicated.

>>8077777
nice quints

>>8077848
You mean it's quite hard if you can't do first year linear algebra?

>>8077777
Not sure if this movie is actually real anymore...

>>8077500
something they cant solve:
-describe a basis of R seen as a vector space over Q

something they can solve but is pretty hard if you don't know how to do it:

if A is a matrix with real coefficients, such as [math]A.A^T.A[/math] is symmetrical, then [math]A[/math] is symmetrical as well.

>>8077934
You guys don't seem to know the meaning of difficult.

>>8077960
then show me your proof.

>>8077500
How do I find a way to align my vector in a qt grills subspace if least squares are not allowed?

>>8077972
Lol, that is your problem lad, not mine.

>>8077971
You mean copy LaTeXing out of linear algebra lecture notes?

>>8077977
I'm pretty sure that if you could solve it, you wouldn't say that because it's not that long.

As expected, you contribute nothing AND you're full of shit.

>>8077934
What's the [math].[/math]?

>>8077988
It's the elementwise product.

>>8077934
You can't build real numbers as linear combinations of fractions since the fractions are closed under addition and multiplication and irrational numbers are real numbers which are not fractions.

>>8077981
Are you fucking kidding me? Hello? Hamel basis? Or it you want, don't use the ZFC and use a Schauder basis?

>>8077988
Isn't that trivial then or am I missing something?
If [math]a^2 b = a b^2[/math] then [math]a = b[/math]

>>8077988
just the regular matrix product

>>8078006
Do transposes always commute, is every matrix invertible?

>>8078021
>Do transposes always commute
For square matrices they do.

>>8078027
What about a matrix with first row of ones and rest zeroes

>>8077934
>if A is a matrix with real coefficients, such as A.AT.A is symmetrical, then A is symmetrical as well.
>difficult
>symmetric
why not generalise and talk about normal matrices?

Hey, here is a question. This might be obvious but how do I find sinus of an angle? (Without knowing the oposit or hypotenus)
Im trying to calculate a speciffic effect in an AC wave

>>8078067
Use a calculator or computer? I believe they use some series expansion to approximate it, which you could do by hand as well.

>>8078074
Yes, thanks for the tip, I havent tried a propper sin calculator yet. Only my iphone calculator which doesnt work.
Wondered if anyone knew how to find the sinus of an angle manualy (by only knowing the degree.)