Definition of an N-tupleDate: 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/ |
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