What does"double-infinities" mean?

[Nipon Waiyaworn]

Hello everyone
Help me please...
What does"double-infinities" mean?

 

[fresh_42]

Hello everyone
Help me please...
What does"double-infinities" mean?

Can you provide some context?

 

[Nipon Waiyaworn]

Can you provide some context?

yes!
context: In a recent article MacKinnon describes four methods that may be used to find square roots of 2*2 matrices. The first of these methods requires that the matrix for which the square roots are sought be diagonalizable and, subsequently, this method was used by Scott to determine all the square roots of 2*2 matrices. A surprising conclusion is that scalar 2*2 matrices possesses double-infinities of square roots whereas non-scalar 2*2 matrices have only a finite number of square roots.
The purpose of this article is to show how the Cayley Hamilton theorem may be used to determine explicit formulae for all the square of 2*2 matrices. These formulae indicate exactly when a 2*@ matrix has square roots, and the number of such roots.
from : DONALD SULLIVAN

 

[S.G. Janssens]

It is still rather unclear, I think. It could for example be a set of square roots indexed by ##\mathbb{Z}##, or a set of square roots indexed by a pair ##(m,n) \in \mathbb{N}^2##, or...

(...) this method was used by Scott to determine all the square roots of 2*2 matrices. A surprising conclusion is that scalar 2*2 matrices possesses double-infinities of square roots whereas non-scalar 2*2 matrices have only a finite number of square roots.

Maybe look up the article by Scott that this abstract refers to? There it is probably explained with "double infinities" exactly means in this context.

 

[Nipon Waiyaworn]

It is still rather unclear, I think. It could for example be a set of square roots indexed by ##\mathbb{Z}##, or a set of square roots indexed by a pair ##(m,n) \in \mathbb{N}^2##, or...

Maybe look up the article by Scott that this abstract refers to? There it is probably explained with "double infinities" exactly means in this context.

From information of the article that I read,
a following example is made by me;
EX1 Find all of square roots of A=[0,0;0,0]
from formula in the article we get
X=[a,b;c,-a] , a^2+bc=0
show that A has a double infinity of square roots
I don't get "A has a double infinity of square roots"

 

[jim mcnamara]

I do not know if this helps:
Nick MacKinnon, Four routes to matrix roots, Mcrtlt. Coz. 73 (19891, 135-136.
Nigel H. Scott, On square-rooting matrices, Math. Gaz. 74 (1990), 111-114.

From Sullivan article:
https://www.maa.org/sites/default/files/Square_Roots-Sullivan13884.pdf

 

[fresh_42]

From information of the article that I read,
a following example is made by me;
EX1 Find all of square roots of A=[0,0;0,0]
from formula in the article we get
X=[a,b;c,-a] , a^2+bc=0
show that A has a double infinity of square roots
I don't get "A has a double infinity of square roots"

I read it as: there are infinitely many values for b and infinitely many values of c which satisfy the equation for a, so double infinitely many. It looks like a parameterization of the solutions. It is a bit unusual to call it this way and I wouldn't spend too much time on it. I don't think there is any value to it.

 

[Nipon Waiyaworn]

I read it as: there are infinitely many values for b and infinitely many values of c which satisfy the equation for a, so double infinitely many. It looks like a parameterization of the solutions. It is a bit unusual to call it this way and I wouldn't spend too much time on it. I don't think there is any value to it.

In simple talk, we can change a to c or b that is there are infinitely many values for b and infinitely many values of a which satisfy the equation for c or, there are infinitely many values for c and infinitely many values of a which satisfy the equation for b. (which don't only satisfy the equation for a) ?
Sorry I use English language that incorrect maybe, I am Thai,am not good in English language. Importantly, I need to have friends that use English language mainly, request for their Facebook,instargram or etc for chatting with them for development in Eng.

 

[Evo]

Sorry I use English language that incorrect maybe, I am Thai,am not good in English language. Importantly, I need to have friends that use English language mainly, request for their Facebook,instargram or etc for chatting with them for development in Eng.

You will get plenty of exposure to English here on the forum, we do not encourage soliciting private contact. Over time, you may make friends, otherwise, it is not safe to solicit and/or give out contact information to strangers on the internet. Our members also do not know who you are I would caution them not to give out their contact information.

 

[Nipon Waiyaworn]

You will get plenty of exposure to English here on the forum, we do not encourage soliciting private contact. Over time, you may make friends, otherwise, it is not safe to solicit and/or give out contact information to strangers on the internet. Our members also do not know who you are I would caution them not to give out their contact information.

I am sorry, I don't know what it is about the rules. You can delete my post.

 

[fresh_42]

I am sorry, I don't know what it is about the rules. You can delete my post.

No need to do so. @Evo's post has been meant as an advise in advance (I think). Beside our forum rules, the reason why they exist is more important than the fact they are rules. This is a public forum, so in principle 7,434,929,364 , 7,434,929,365 , 7,434,929,366 , 7,434,929,367 ... people can read everything. I do not speculate on potential aliens visiting our planet which could read them as well, as such a hypothesis must not be discussed here either, for, which I believe, obvious reasons. Anyway, these are a lot of people and, sorry to tell you that, some of them are really mean and evil. You do not want to get in touch with them and even less, that they will know private data of yours. The possibilities to abuse them are manifold in these times. So that is the reason why we try to prevent the exchange of data of this kind. Too high are the dangers on the internet.

And as @Evo said: you can participate in a lot of discussions here, scientific ones as well as entertaining ones, which give you plenty of opportunities to practice English ... at least a kind of ... but this wouldn't be a better English on Skype ... so what ...