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An orthogonal array is simple if it does not contain any repeated rows. (Subarrays of t columns may have repeated rows, as in the OA(18, 7, 3, 2) example pictured in this section.) An orthogonal array is linear if X is a finite field F q of order q (q a prime power) and the rows of the array form a subspace of the vector space (F q) k. [2]
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 ...
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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
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]
Three orthogonal planes slice a cake into at most eight (C 3) pieces Animation showing the cutting planes required to cut a cake into 15 pieces with 4 slices (representing the 5th cake number). Fourteen of the pieces would have an external surface, with one tetrahedron cut out of the middle.
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
The set of all orthogonal matrices of size n with determinant +1 is a representation of a group known as the special orthogonal group SO(n), one example of which is the rotation group SO(3). The set of all orthogonal matrices of size n with determinant +1 or −1 is a representation of the (general) orthogonal group O(n).