Notation for Representing Arrays in Math Research

[elusiveshame]

I apologize if this is in the wrong forum, but I'm not quite sure there's a category where this would fit in.

Anyway, I'm doing an independent research/analysis of the RGB color space, and as I'm writing down my formulas and algorithms, I want to express in the math that certain variables are arrays, and in some cases, array vectors.

My question is, is there any notation specifically for arrays? What I've been using to mark the vectors that are arrays, is putting an x and y on the left side of the vector, like a division problem, just without the line in between.

If there isn't any notation used in any formal math subjects, would this be an acceptable method, as long as it's stated in the report?

Thanks!

 

[Mark44]

I apologize if this is in the wrong forum, but I'm not quite sure there's a category where this would fit in.

Anyway, I'm doing an independent research/analysis of the RGB color space, and as I'm writing down my formulas and algorithms, I want to express in the math that certain variables are arrays, and in some cases, array vectors.

My question is, is there any notation specifically for arrays? What I've been using to mark the vectors that are arrays, is putting an x and y on the left side of the vector, like a division problem, just without the line in between.

If there isn't any notation used in any formal math subjects, would this be an acceptable method, as long as it's stated in the report?

Thanks!

AFAIK, the term "array" is used mostly in programming contexts and the terms "vector" and "matrix" are used mostly in mathematics. Arrays can be one-dimensional, and therefore synonymous with vectors, or they can be two-, three-, or higher dimensional.

How are you using the term "array?" If you are using this term to mean a matrix, you could define a matrix A like so: $A \in M_{4x4}$, which says that A is an element of the set of 4 X 4 matrices.

The usual vector notation uses an arrow above the variable, like this:
$$\vec{v}$$

 

[elusiveshame]

Thanks for the reply. I'm about to leave work shortly, but I'll respond with a picture of how I'm currently writing it and to answer your question

 

[elusiveshame]

AFAIK, the term "array" is used mostly in programming contexts and the terms "vector" and "matrix" are used mostly in mathematics. Arrays can be one-dimensional, and therefore synonymous with vectors, or they can be two-, three-, or higher dimensional.

How are you using the term "array?" If you are using this term to mean a matrix, you could define a matrix A like so: $A \in M_{4x4}$, which says that A is an element of the set of 4 X 4 matrices.

The usual vector notation uses an arrow above the variable, like this:
$$\vec{v}$$

I'm using the term array as the programming term, just unbounded in the formula's since these can be applied in several theories and such for programming. Since I wasn't sure of the proper way to write the notations, I sort of combined what I know in the world of math (single variable calculus is the highest math education I've received so far) with programming structure, or at least in a way that makes perfect sense to me :P

Since I'm not familiar with the forums math functionality and how to use it, I drew up what I was talking about in MS Paint :)

That's how I'm currently notating it. I guess the easiest way to explain it would be saying it's a double vector, so for example the vector C is the color and contains the R, G, and B values, and C would be a part of a Pixel vector at coordinates X, Y and would be the actual RGB value.

Actually, after writing down what I'm trying to do instead of just keeping it in my head, I guess the question should be revised to: Can vectors contain a vector for one of its components? Like, could $$\vec{v}$$ contain $$\vec{c}$$ as one of it's components, and if so, how would you notate it?

And as a sub question, if I were to post my paper on my own website, would viewers see me as completely wacko for using something like I've been doing, or would it be acceptable to do something like that, as long as it's defined in the document?

Thanks :)

 

[Mark44]

What do you mean by "double vector?" I think that plain old vectors should work just fine.

$$ \vec{v} = \begin{bmatrix} c_R \\ c_G \\ c_B \\ P_x \\ P_y \\ P_z \end{bmatrix}$$

The vector above has the red, green,and blue components of the color of a pixel in its first three coordinates, and the x, y, and z components of the position of the pixel in its last three coordinates.

The notation you created in Paint seems needlessly convoluted to me. If something simpler will serve the purpose, there's no reason to use complex notation, unless the goal is to obfuscate things.

 

[elusiveshame]

What do you mean by "double vector?" I think that plain old vectors should work just fine.

$$ \vec{v} = \begin{bmatrix} c_R \\ c_G \\ c_B \\ P_x \\ P_y \\ P_z \end{bmatrix}$$

The vector above has the red, green,and blue components of the color of a pixel in its first three coordinates, and the x, y, and z components of the position of the pixel in its last three coordinates.

The notation you created in Paint seems needlessly convoluted to me. If something simpler will serve the purpose, there's no reason to use complex notation, unless the goal is to obfuscate things.

I meant nested, not double, sorry :p

Could your example be written as: $$ \vec{v} = |C,P| (with vector notation for C and P)?

(sorry, the matrix either doesn't like vectors inside of it, or I'm just doing it wrong)

 

[Mark44]

I meant nested, not double, sorry :p

Could your example be written as: $$ \vec{v} = |C,P| (with vector notation for C and P)?

You could, but why would you want to? I get the sense that you want to use notation just to use notation, and not to clarify or simplify things. If you have a vector whose elements are themselves vectors, then you're really talking about a two-dimensional matrix. If A is such a matrix, and the indexes for the rows run from 1 to 3, then A(1, 2) would be the y coordinate of a particular pixel and A(2, 1) would be the green value of a pixel.

A more natural container for this information might be a structure (or struct in C, C++, etc.). One element of the struct could be an array of RGB values, and another element could be the x, y, and z coordinates. If you have an instance of this struct named pixel, you could access the colors by pixel.RGB[red], and the position by pixel.Position[x], for example.

(sorry, the matrix either doesn't like vectors inside of it, or I'm just doing it wrong)

 

[elusiveshame]

It was more out of curiosity and understanding. I just didn't think of it as the way you put it and was trying to define them separately when there's no need to. After thinking about it some more, you're right, I was over complicating it, which is why it led to this thread :P So, thank you for that! :D

Also, you're right about the struct example, that's exactly what how I'm doing it in VB :)