[a. F. orthogonal, f. orthogone: see prec. and -al1; and cf. hexagonal, etc.]
1. Having or of the nature of a right angle, right-angled (obs.); pertaining to or involving right angles; at right angles to something else, or to each other; rectangular.
orthogonal projection, projection in which the rays are at right angles to the plane of projection. orthogonal trajectory, a curve intersecting each of a family of curves at right angles.

2. Math. a. Of a linear transformation: preserving lengths and angles; leaving unchanged quantities of the form x1^2 + x2^2 +…+ xn^2 and the inner product of any two vectors.

b. Applied to the group of all orthogonal matrices of a given order.

c. Of a square matrix: representing an orthogonal transformation; such that the rows (and likewise the columns) are orthonormal when considered as vectors; equal to the inverse of its transpose; (these three properties are equivalent).

d. Of two vectors or functions: perpendicular; having an inner product equal to zero. Of a set of vectors or functions: such that the inner product of any two is zero if and only if the two are distinct.

3. Statistics. Of a set of variates: statistically independent. Of an experimental design: such that the variates under investigation can be treated as statistically independent.

brendon@phi:~$ dict ortho1 definition foundFrom The Collaborative International Dictionary of English v.0.48 [gcide]:  Ortho- \Or"tho-\ ([^o]r"th[-o]-) pref. [Gr. ''orqo`s straight;     akin to Skr. [=u]rdhva upright, v[.r]dh to grow, to cause to     grow.]     [1913 Webster]     1. A combining form signifying straight, right, upright,        correct, regular; as, orthodromy, orthodiagonal, orthodox,        orthographic.        [1913 Webster]     2. (Chem.) A combining form (also used adjectively),        designating:        (a) (Inorganic Chem.) The one of several acids of the same            element (as the phosphoric acids), which actually            occurs with the greatest number of hydroxyl groups;            as, orthophosphoric acid. Cf. {Normal}.        (b) (Organic Chem.) Connection with, or affinity to, one            variety of isomerism, characteristic of the benzene            compounds; -- contrasted with {meta-} or {para-}; as,            the ortho position; hence, designating any substance            showing such isomerism; as, an ortho compound.            [1913 Webster]     Note: In the graphic representation of the benzene nucleus           (see {Benzene nucleus}, under {Benzene}), provisionally           adopted, any substance exhibiting double substitution           in adjacent and contiguous carbon atoms, as 1 & 2, 3 &           4, 4 & 5, etc., is designated by ortho-; as,           orthoxylene; any substance exhibiting substitution of           two carbon atoms with one intervening, as 1 & 3, 2 & 4,           3 & 5, 4 & 6, etc., by meta-; as, resorcin or           metaxylene; any substance exhibiting substitution in           opposite parts, as 1 & 4, 2 & 5, 3 & 6, by para-; as,           hydroquinone or paraxylene.           [1913 Webster]