I GOT IT!

IT WORKS

sort of

@Alizter, how does that image visually represent $D_{100}$?

@KajHansen Look.

A friend helped me.

@PedroTamaroff, I think I solve a slightly different problem. I thought it was "all diagonal elements equal OR all subdiagonal elements equal".

@Studentmath what does a biostat. do or write ? How are the studies like ?

Oh, it asks for both. =P

@Charlie mylady

I think my solution can be salvaged nevertheless. Let me think, and I'll report back.

I never saw your solution.

I'm interested.

haha, I've been holding out because I didn't want to give anything away if you were thinking about it

@mick hi, I was having a chat with myself

@Charlie do you like yourself ?

@mick yes I like

@PedroTamaroff, unfortunately it looks like the "and" requirement messes things up.

But here was the gist of my solution:

@Charlie do you play with yourself often ?

lol im badass

Imagine that the requirement was "or" instead. Then m = 2 corresponds with n = 2. This is because the subdiagonal is always homogeneous (there is only 1 subdiagonal entry).

@mick no you're not a badass, just nonsense

Now suppose for some $m$, there exists an $n$ such that the property holds. Now we need to show that such an $n$ exists for $m+1$

@Charlie i like to play with myself

The way that you can do that is as follows:

@mick ok

@mick Feynman once wrote: Math is to Physics as masturbation is to sex

Say you need an $n \times n$ matrix to guarantee an $m \times m$ submatrix.

@skullpatrol i think it's more like a torture

Now start with a $2n+1 \times 2n+1$ matrix.

@skullpatrol no seks is better , but physics is not.

@Charlie that's because you're not Feynman :-)

@KajHansen OK.

You can partition this matrix into three pieces. The first piece is an $n \times n$ submatrix in the bottom left corner. The second is an $n \times n$ piece in the top right, and the third is a thin strip of a single column and single row.

@mick but they are similar

Now by the induction hypothesis, you can transform the bottom left into a $m \times m$ matrix with the property without affecting the top right corner whatsoever.

@skullpatrol yeah he was not mathematician

Likewise, you can do the same with the top right corner without affecting the bottom left whatsoever.

@skullpatrol without ac yes.

The thin strip of one column/one row is simply there to guarantee that there will be at least one $1$ or one $0$ along the diagonal in the top right.

@Charlie he could have been

AC of single men : you can choose any single women within a small radius.

@skullpatrol but he wasn't

Anyways, you'll have two $m \times m$ matrices in this reduced form touching diagonally. From there, you take a few simple cases and you can always be guaranteed an $m+1 \times m+1$ matrix with diagonal entries equal.

@skullpatrol no

@Charlie neither was Einstein

It's pretty hard to explain without a blackboard unfortunately, and I have no motivation to draw MSpaint pictures since I was interpreting the problem incorrectly, lol

@skullpatrol he could have been

@skullpatrol indeed

@Charlie Only Newton was both.

@skullpatrol no

@skullpatrol newton is a myth

No, a legend.

myth

legend

lol Leibniz rule , maxwell equations , should have been disc by newton !

infinite descent , double slit

too

no one else was that good at both

he was good but overhyped.

and Einstein isn't?

@skullpatrol fermat

we are talking about ability in BOTH

@skullpatrol no

Euler

what part of BOTH don't you understand?

@skullpatrol fermat did not publish but he did both

@Charlie +1

Feynman had great ability in both.

@mick in ancient times, everyone studied everything

look gauss

GAUSS IS EVERYWHERE

lets face it , newton did interpolation , iteration and infinitesimal "basics " thats all math.

PHYSICS, MATHEMATICS, STATISTICS

@Charlie gauss was the " real " newton

@mick Gauss was the greatest no doubt

agreed^ in math

in many subject

@Charlie my friend claims to be the new gauss :)

@mick he's dumbass

Cauchy was awesome too

@Charlie best till 1880

@skullpatrol yes

please, skull, don't come with that newton's ball licking

@Charlie i love it when you talk dirty :)

LOL

oo charlie ...

>:(

:p

star me baby :)

I'm pissed off today

Does anyone here like combonotorocs ??

@Charlie that dumbass generalized ideas of Cauchy ...

@Bananarama, kombinatorix is pretty cool sometimes.

@Charlie sorry ?

@mick i learned one thing: study a subject with the one who wrote it will eventually make me feel very depresed

@Bananarama what is it?

sorry to have hormones @Charlie

combinatorics

cobnohoriks

@mick you have hormones too, you imbecile, go study some biology first

calkoeloes and algubre

@Bananarama ah

@Charlie i said sorry for MY hormones

why do girls get angry when you flirt ? biologically very wrong strategy.

human bio is inefficient contrary to common belief

silence .........

im gonna get banned from chat again right :)

no

you upset

yes

Soo.. Good night!

goodnight