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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 ...
Orthogonal array testing is a systematic and statistically-driven black-box testing technique employed in the field of software testing. [ 1 ] [ 2 ] This method is particularly valuable in scenarios where the number of inputs to a system is substantial enough to make exhaustive testing impractical.
An alternate representation of a Latin square is given by an orthogonal array. For a Latin square of order n this is an n 2 × 3 matrix with columns labeled r, c and s and whose rows correspond to a single position of the Latin square, namely, the row of the position, the column of the position and the symbol in the position. Thus for the order ...
An orthogonal array, OA(k,n), of strength two and index one is an n 2 × k array A (k ≥ 2 and n ≥ 1, integers) with entries from a set of size n such that within any two columns of A (strength), every ordered pair of symbols appears in exactly one row of A (index). [33] An OA(s + 2, n) is equivalent to s MOLS(n). [33]
Visual understanding of multiplication by the transpose of a matrix. If A is an orthogonal matrix and B is its transpose, the ij-th element of the product AA T will vanish if i≠j, because the i-th row of A is orthogonal to the j-th row of A. An orthogonal matrix is the real specialization of a unitary matrix, and thus always a normal matrix.
If each entry of an n × n Latin square is written as a triple (r,c,s), where r is the row, c is the column, and s is the symbol, we obtain a set of n 2 triples called the orthogonal array representation of the square. For example, the orthogonal array representation of the Latin square
In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows: In random sampling new sample points are generated without taking into account the previously generated sample points. One does not necessarily need to know beforehand how many sample points are needed.
The orthogonal group is an algebraic group and a Lie group. It is compact. The orthogonal group in dimension n has two connected components. The one that contains the identity element is a normal subgroup, called the special orthogonal group, and denoted SO(n). It consists of all orthogonal matrices of determinant 1.