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In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array) is a "table" (array) whose entries come from a fixed finite set of symbols (for example, {1,2,...,v}), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these ...
Given a quasigroup Q with n elements, its Cayley table (almost universally called its multiplication table) is an (n + 1) × (n + 1) table that includes borders; a top row of column headers and a left column of row headers. Removing the borders leaves an n × n array that is a Latin square. This process can be reversed, starting with a Latin ...
The following list contains syntax examples of how a range of element of an array can be accessed. In the following table: first – the index of the first element in the slice; last – the index of the last element in the slice; end – one more than the index of last element in the slice; len – the length of the slice (= end - first)
For algorithms and data structures not necessarily mentioned here, see list of algorithms and list of data structures. This list of terms was originally derived from the index of that document, and is in the public domain, as it was compiled by a Federal Government employee as part of a Federal Government work. Some of the terms defined are:
Structures (but not arrays) may be returned from a function. An array can be returned if it is inside a structure. A member of a structure can be any data type (except void, or the structure of the same type). An array element can be any data type (except void). Everything is passed by value (except arrays).
orthogonal group: real orthogonal matrices: Y Z 2 – The symmetry group of the sphere (n=3) or hypersphere. so(n) n(n−1)/2 SO(n) special orthogonal group: real orthogonal matrices with determinant 1 Y 0 Z n=2 Z 2 n>2 Spin(n) n>2 SO(1) is a single point and SO(2) is isomorphic to the circle group, SO(3) is the rotation group of the sphere. so(n)
A block matrix which is essentially a tridiagonal matrix but with submatrices in place of scalar elements. Boolean matrix: A matrix whose entries are taken from a Boolean algebra. Cauchy matrix: A matrix whose elements are of the form 1/(x i + y j) for (x i), (y j) injective sequences (i.e., taking every value only once). Centrosymmetric matrix
The arrays are heterogeneous: a single array can have keys of different types. PHP's associative arrays can be used to represent trees, lists, stacks, queues, and other common data structures not built into PHP. An associative array can be declared using the following syntax: