Definition of an N-tuple

Date: 09/20/1999 at 22:26:54
From: Matt Warner
Subject: N-tuple

What is an n-tuple? I'm reading a book on computer algorithms, 
specifically a section on "backtracking." The section talks about 
n-tuples such as "... the desired solution is expressible as an 
n-tuple (x1, ..., xn)" but I can't find a definition of an n-tuple (or 
tuple) anywhere.

Date: 09/29/1999 at 22:42:49
From: Doctor TWE
Subject: Re: N-tuple

Hi Matt. Thanks for writing to Dr. Math. 

The term n-tuple is primarily used in linear algebra to refer to a 
1-dimensional matrix of n elements. For example; [1 2], [21 -4] and 
[-1 0] are 2-tuples; [1 2 3], [0 -2 6] and [-1 0 -1] are 3-tuples; and 
so on. These are row matrices (because it's easier to write them as 
text), but "tuples" can also refer to column matrices, so

                     +-   -+
     +-   -+         | -1  |
     |  2  |         |     |
     |     |   and   |  9  |
     |  0  |         |     |
     +-   -+         |  7  |
                     +-   -+

are examples of a 2-tuple and a 3-tuple as well.

One of the most common uses of tuples in linear algebra is to 
represent vectors. The 2-tuple [3 -1], for example, could represent a 
vector in two-dimensional space whose tail is at the origin and whose 
head is at the Cartesian point (3,-1). The 3-tuple [-1 2 -4] could 
represent a vector in three-dimensional space whose tail is at the 
origin and whose head is at the Cartesian point (-1,2,-4). This allows 
us to manipulate vectors using the rules of matrix arithmetic. It also 
allows us to easily work with vector spaces larger than three 
dimensions without getting bogged down in "visualization" problems.

I hope these examples help. Write back if you have any other 
questions.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/