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In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

The orthogonal complement of a subspace V of the vector space R^n is the set of vectors which are orthogonal to all elements of V. For example, the orthogonal complement of ...

The orthogonal decomposition of a vector y in R^n is the sum of a vector in a subspace W of R^n and a vector in the orthogonal complement W^_|_ to W. The orthogonal ...

A projection of a figure by parallel rays. In such a projection, tangencies are preserved. Parallel lines project to parallel lines. The ratio of lengths of parallel segments ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthogonal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. Note ...

An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an ...

The orthographic projection is a projection from infinity that preserves neither area nor angle. It is given by x = cosphisin(lambda-lambda_0) (1) y = ...

The orthojoin of a point X=l:m:n is defined as the orthopole of the corresponding trilinear line lalpha+mbeta+ngamma. In other words, the orthojoin of Kimberling center X_i ...

An orthonormal set is a set of normalized orthogonal vectors or functions.

The orthopoles of a line l with respect to the four triangles formed by three out of four vertices of any quadrilateral ABCD lie on a straight line L known as the orthopolar ...