Hey guys. Kinda' dumb question that might not make sense. If we have two matrices A and B, and we have the expression A^T B. Is it equivalent to BA in any way?

No

Unrelated expressions

The coefficients in A^T B look like [row of A^T] * [column of B], or a dot product [column of A] * [column of B]

The coefficients in BA look like [row of B] * [column of A]

Note the mismatch here --- in one of your expressions you look at columns of B; in the other, rows

(I'm assuming these things are square matrices or there's no reason your two expressions should even be defined!)

What is true in general is that A^T B = (B^T A)^T

@TedShifrin you don't have to!

@MikeMiller which does mean that BA is the transpose of A^T B if B happens to be symmetric. but that's about it

true :) but that fits with the above explanation, too, since the issue was that rows of B and columns of B are unrelated in general

for B symmetric they coincide

Sigh okay

I am a little stuck. I am trying to solve the functional equation $f(z+1) = zf(z)$ without resorting to the Gamma function. This exercise has led me to a $g$ such that $g(z+1) = ze^ag(z)$, so I think it wants me to use $g$, but I can't think of a way of using the same trick that is often used for the Gamma function because that one builds it from a $g$ such that $g(z-1) = ze^ag(z)$.

what exactly do you mean by "solve"

Find an explicit solution for $f$.

Any solution, doesn't have to be unique of course (I don't think it is). The Gamma function is of course one.

And the zero function. :P

I have a question. There is a post that askes an interesting question about using 1/0. normally dividing be 0 is not allowed but in the post's Comments $[here]math.stackexchange.com/questions/4047738/… $ someone mentions Wheel theory. I have never herd of such a thing and it allows for division to always be defined. Why would we down vote this instead of show off it relates to a different mathematics?

There's also transfinite arithmetic

The BBC wrote an article on some computer scientist who had "solved the problem of dividing by zero by introducing a new number off the real line called 'nullity'"

Cool, I find it interesting, but the Question is why would we downvote it instead of showcasing it?

@OneColdRuben it gets downvoted because they assert their 1=2 proof holds in what seems to be a context other than wheels. While wheels are a thing, their proof doesn't hold in a wheel.

Oh ok.

As well, we can't expect everyone to know about wheels.

So of course some people might mention wheels, but some people might not know about them and not think of the opportunity.

Are the only people to use this site PHD's and some such related in acidemia?

Not at all.

Generally a wide range from high school to academia. But academia level questions usually get asked on mathoverflow

I am new to this and knew nothing about that site either. Heck I am looking at dishing out money to a tutor in a Masters level Math Logic course on another new site. I never knew that all these things existed (the sites). I guess you never know until you do, is a true statement.

You could just not study logic

Right, No choice. Last semester of Math education, small school, no other offered classes. No option.

Sad

(I was only joking, for the record, study what you want)

@OneColdRuben don't dish out money for a tutor until you try by yourself. ;)

Yes. It is sad, frustrating, blah blah blah. Oh good point, I never thought about just doing it myself.

Researching online, reading my books, talking to strangers on math websites I have never known about, it just didn't hit me that everything I need to know I already knew.

Come on.

It hit me that I cant do it alone and I better ask for help before I am crushed.

He wasn't picking on you... he was just saying that he wasn't serious when he said one shouldn't study logic. No need to be sarcastic.

Oh, sorry.

I just was pointing out how it sounded.

@MikeMiller I think he was referring to anakhro's comment on not getting a tutor until he tried on his own, but your point still stands I think

@OneColdRuben asking questions is always a good idea btw, admitting to yourself that you can't do something alone is a step towards success

sorry, yes, I don't know how to directly reply, The sarcasm was directed at the comment by Anakhro. Edward thank you. Everyone thank you, I understand that this is not the place for sarcasm, and I should have just pointed it out as a comment I disagreed with.

Nah be as sarcastic as you want, there's so much shit-talk here you wouldn't believe

It#s all in good faith tho

Oh. There are times that I don't understand the culture I live in.

@OneColdRuben have you been to speak with the professor already?

Office hours are notoriously underused.

Yes the times we have available do not line up. Even outside office hours, I work full time and have a family with 2 kids. My son is only 1.5 years old. just this semester and the summer to be done.

Respect

Sorry I am trying to say I will be done with my degree after this summer.

Luckily this is my time at work, chatting on here. I do have to say the site is really intimidating.

Also thank you, Edward.

Don't worry, the questions site gives you answers to all your homework without asking you to do any of the work.

It's only in this chat that real learning takes place.

@OneColdRuben let's hope the previous exchange didn't give you a bad impression of this chatroom full of brilliant minds.

lmao

This claim about brilliancy is disputed

Haken released an album called virus in 2020

oof

Metal musicians are in on it

Governments knew that nobody listens to cattle decapitation so they drafted them to write songs about the return of the plague so they could claim they informed the public

you heard it here first

Hullo @Ted

Howdy, @Edward

@EdwardEvans Haken's previous album was called vector

And the name for virus was decided long before the pandemic

They knew beforehand confirmed

Haken infected a bat in China confirmed

I'm considering finishing my masters by taking loads of credits in compsci and arithmetic of abelian varieties so I can go into crypto

I feel like this is a better idea than just quitting and trying to get a job in software dev

but I got some time to decide and I still have funding to burn through

TED

@anakhro?

@TedShifrin do you have time to provide a small hint.

If possible, that is.

How can you avoid the Gamma function when that (together with an initial value) characterizes it?

To be honest, I haven't thought about this sort of stuff since I taught it in the 80s.

And I don't understand your $e^ag(z)$.

I thought it also needed log convexity

I honestly don't remember.

Have you looked at the standard texts?

Yeah. That's the Bohr-Mollerup theorem.

log convexity, f(z+1)=zf(z), f(1) = 1 defines the Gamma function

Ah, OK. Well, as I said, I haven't thought about this in almost 40 years. I pass.

D:

If you want to talk about Chern classes or Riemann-Roch, let me know. :)

How do you say Roch? Rock?

Is Roch french?

Like the Scottish "Loch"

So like rock

I'm trying to think of an English approximation

not K at the end.

Edward be right.

It's German, not English.

Rock and Loch are rhymes. Räk and läk

Like this but with an R at the start

Rkoch ?

HAHAHA

nah

sry I had to

lma

o

How is it going?

Rather not say

you?

not too bad