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A mathematical object upon which an operator acts. For example, in the expression 1×2, the multiplication operator acts upon the operands 1 and 2.

A simple way to enumerate some types of groups due to J. H. Conway (Zwillinger 1995).

A nonsingular linear map A:R^n->R^n is orientation-reversing if det(A)<0.

A bicupola in which the bases are in the same orientation.

Coordinates defined by an orthocentric system.

A cupolarotunda in which the bases are in the same orientation.

Two or more lines or line segments which are perpendicular are said to be orthogonal.

Two subspaces S_1 and S_2 of R^n are said to be orthogonal if the dot product v_1·v_2=0 for all vectors v_1 in S_1 and all v_2 in S_2.

Orthogonal contravariant and covariant satisfy g_(ik)g^(ij)=delta_k^j, where delta_j^k is the Kronecker delta.

Unit vectors which are orthogonal are said to be orthonormal.