Array (Subscripted Variable) Definition/Meaning:
An ordered collection of a number of elements of
the same type, the number being fixed unless the array is flexible. The
elements of one array may be of type integer, those of another array may be of
type real, while the elements of a third array may be of type character string
(if the programming language recognizes compound types). Each element has a
unique set of index values that determine its position in the ordered
collection. Each index is of a discrete type. The number of dimensions in the
ordering is fixed.
A one-dimensional array, or vector, consists of a list of elements
distinguished by a single index. If v is a one-dimensional array and i is an
index value, then vi refers to the ith element of v. If the index ranges from L
through U then the value L is called the lower bound of v and U is the upper
bound. Usually in mathematics and often in mathematical computing the index type
is taken as integer and the lower bound is taken as one.
In a two-dimensional
array, or matrix, the elements are ordered in the form of a table comprising a
fixed number of rows and a fixed number of columns. Each element in such an array is distinguished by a pair of indexes. The first index
gives the row and the second gives the column of the array in which the element
is located. The element in the ith row and jth column is called the i,jth element
of the array. If i ranges from L1 through U1 and; ranges from L2 through U2 then
L1 is the first lower bound of the array, U1 is the first upper bound, L2 is the
second lower bound and U2 is the second upper bound. Again it is common practice
to take the indexes as integers and to set both LI and L2 equal to one.
In three-dimensional arrays the position of each element is distinguished by
three indexes. Arrays of higher dimension are similarly defined.
