3x3 Diagonalizable Matrices over GF(2)

[ArcanaNoir]

It appears to turn into a higher order polynomial expression.
It may not be possible to solve that.
At any rate, Wolfram doesn't.

Neither will maple. Although maple sucks at algebraic manipulation.

 

[I like Serena]

I just noticed that this sub forum for abstract algebra is now moderated by Mark44 and Fredrik.
... but neither of those two is high up into abstract algebra.
It seems micromass has left some sort of vacuum here...

 

[micromass]

Mark44 and Fredrik certainly know their abstract algebra. Mark44 has a masters in math (and maybe more), so he's more than capable. And I've seen Fredrik make some very good abstract algebra posts.

Besides, you don't need to be an expert in a subject to be able to moderate something well. I'm certainly no expert in abstract algebra related things, but I did feel like I had no trouble moderating it.

 

[I like Serena]

Mark44 and Fredrik certainly know their abstract algebra. Mark44 has a masters in math (and maybe more), so he's more than capable. And I've seen Fredrik make some very good abstract algebra posts.

Besides, you don't need to be an expert in a subject to be able to moderate something well. I'm certainly no expert in abstract algebra related things, but I did feel like I had no trouble moderating it.

I'm sorry.
I didn't mean to criticize you or Mark44 or Fredrik.
My remark was more intended as a compliment to you, since I do consider you to be high up.

 

[ArcanaNoir]

I just noticed that this sub forum for abstract algebra is now moderated by Mark44 and Fredrik.
... but neither of those two is high up into abstract algebra.
It seems micromass has left some sort of vacuum here...

Mark44 and Fredrik certainly know their abstract algebra. Mark44 has a masters in math (and maybe more), so he's more than capable. And I've seen Fredrik make some very good abstract algebra posts.

Besides, you don't need to be an expert in a subject to be able to moderate something well. I'm certainly no expert in abstract algebra related things, but I did feel like I had no trouble moderating it.

Yeah I don't think who the moderator is makes much difference, it seems like everyone tries to answer whatever they can. It's not like only moderators answer questions and only in their own forums. Besides, I didn't even put it in the algebra forum. As micro said, it feels like I might be able to solve it with "the math we used to call algebra before we learned about abstract algebra and which now seems to lack an appropriate designation".

 

[HallsofIvy]

They need not be invertible.



I'm confused about this, first you say the main diagonal can only have non-zero entries, but then you say the main diagonal can have 0's or 1's. Also, diagonalizable is not the same as diagonal, right?

IlikeSerena made a slight grammatical error.

He/she said "the main diagonal can only have non-zero entries". What he/she meant to say was "only the main diagonal can have non-zero entries". The position of the word "only" is crucial!

 

[ArcanaNoir]

IlikeSerena made a slight grammatical error.

He/she said "the main diagonal can only have non-zero entries". What he/she meant to say was "only the main diagonal can have non-zero entries". The position of the word "only" is crucial!

thanks for the clarification :)