A+ emphasizes partitions where the lower dimensional arrays lie along a set of trailing axes. The lower dimensional arrays that comprise such a partition are called cells. The complementary set of leading axes is called the frame of the partition that holds the cells; the cells are said to be in their frame. In the case of the numeric matrix of bond prices, the row vectors are the cells of rank 1, and the first axis is their frame.
Every set of leading axes defines a partition into cells for which it is the frame. The set of all axes is a particular set of leading axes, and therefore defines a partition. Since there are no axes left for the cells, the cells must be the elements of the array; the A+ notion of cell, then, includes the more common one. At the other extreme, the array itself is a cell, i.e., a partition of itself into one subarray. In this case the cell takes all the axes and therefore the frame has no axes.
A cell consists of all those elements that have one particular set of indices for the leading
axes that define the partition, and all possible indices for the trailing axes. The entire
cell can be selected by specifying only the particular indices for the leading axes. Those
leading axes are the frame of the partition, and therefore the frame is, loosely speaking,
an array of cells that can be indexed by valid indices of them. A partition creates, then,
a view of an array as a frame of cells. There is more about frames and cells, including
several examples, later in this chapter. The
"Dyadic Operators" chapter, and especially its
"Rank Deriving Dyadic" section, has a further
discussion of this subject, with examples.
One partition plays a special role in A+, the one defined by the first axis alone; the cells for this partition are called the items of an array. Every array can be regarded as a vector of items, and many A+ functions look at them in just that way. In such a context, a scalar is regarded as having a single item, namely itself.