MHB What is a Quinary Vector and How is it Related to Matrices?

[Sudharaka]

Hi everyone, :)

Reading a research article, I came across something called a Quinary Vector. I found no explanation or definition of what this means in the article or in the web. The article has the following as a Quinary vector, and it seems like a particular kind of matrix.

$$\begin{pmatrix}0&0&0\\0&0&1\\&.&\\&.&\\&.&\\&.&\\4&4&4\end{pmatrix}$$​

So I would like to see a precise definition of what a Quinary vector means. Has anybody come across this vector before?

 

[I like Serena]

Hi everyone, :)

Reading a research article, I came across something called a Quinary Vector. I found no explanation or definition of what this means in the article or in the web. The article has the following as a Quinary vector, and it seems like a particular kind of matrix.

$$\begin{pmatrix}0&0&0\\0&0&1\\&.&\\&.&\\&.&\\&.&\\4&4&4\end{pmatrix}$$​

So I would like to see a precise definition of what a Quinary vector means. Has anybody come across this vector before?

Hey Sudharaka!

From wikipedia:

Quinary (base-5) is a numeral system with five as the base.​

It seems to me a matrix with all possible combinations of 0-4.
It would probably have $5^3=125$ rows. Or perhaps those rows are meant to represent base-5 numbers.
It's possible that when multiplying it, the numbers might be counted in base 5.
I don't know why they call it a "vector". Perhaps that becomes clear from the context?

 

[Sudharaka]

Hey Sudharaka!

From wikipedia:

Quinary (base-5) is a numeral system with five as the base.​

It seems to me a matrix with all possible combinations of 0-4.
It would probably have $5^3=125$ rows. Or perhaps those rows are meant to represent base-5 numbers.
It's possible that when multiplying it, the numbers might be counted in base 5.
I don't know why they call it a "vector". Perhaps that becomes clear from the context?

Thank you for the reply. :)

Yeah, I think this is the most probable thing that the writer meant. Here is the article which I found this (page 59).

http://www.mecs-press.org/ijcnis/ijcnis-v4-n5/IJCNIS-V4-N5-7.pdf

I don't think that the numbers are counted in base 5 when multiplying. He forms a collection of series which he calls basins by multiplying this vector with a circulant matrix. I don't quite understand how the basins are formed though. :p

 

[Olga]

I cannot understand how the basins are formed either! Has anybody figured that?

 

[caffeinemachine]

I cannot understand how the basins are formed either! Has anybody figured that?

Did you mean 'basis'?

 

[Olga]

Did you mean 'basis'?

No, I indeed mean “basins”. They are discussed on page 59. There is a link to it in the thread.

 

[caffeinemachine]

No, I indeed mean “basins”. They are discussed on page 59. There is a link to it in the thread.

Oh I see. Sorry for the confusion.