Orthogonal Explanation
orthogonal Explanation
Other meanings of the word orthogonal evolved from its earlier use in mathematics.
Art
In art the perspective imagined lines pointing to the vanishing point are referred to as 'orthogonal lines'.
Formally, two vectors x and y in an inner product space V are orthogonal if their inner product is zero. This situation is denoted .
Two vector subspaces A and B of vector space V are called orthogonal subspaces if each vector in A is orthogonal to each vector in B. The largest subspace that is orthogonal to a given subspace is its orthogonal complement.
A linear transformation is called an orthogonal linear transformation if it preserves the inner product. That is, for all pairs of vectors x and y in the inner product space V,
This means that T preserves the angle between x and y, and that the lengths of Tx and x are equal.
A term rewriting system is said to be orthogonal if it is left-linear and is non-ambiguous. Orthogonal term rewriting systems are confluent.
The word normal is sometimes also used in place of orthogonal. However, normal can also refer to unit vectors. In particular, orthonormal refers to a collection of vectors that are both orthogonal and normal (of unit length). So the orthogonal usage of the term normal is often avoided.
In some contexts, two things are be said to be orthogonal if they are mutually exclusive.
Other meanings of the word orthogonal evolved from its earlier use in mathematics.
Art
In art the perspective imagined lines pointing to the vanishing point are referred to as 'orthogonal lines'.
Formally, two vectors x and y in an inner product space V are orthogonal if their inner product is zero. This situation is denoted .
Two vector subspaces A and B of vector space V are called orthogonal subspaces if each vector in A is orthogonal to each vector in B. The largest subspace that is orthogonal to a given subspace is its orthogonal complement.
A linear transformation is called an orthogonal linear transformation if it preserves the inner product. That is, for all pairs of vectors x and y in the inner product space V,
This means that T preserves the angle between x and y, and that the lengths of Tx and x are equal.
A term rewriting system is said to be orthogonal if it is left-linear and is non-ambiguous. Orthogonal term rewriting systems are confluent.
The word normal is sometimes also used in place of orthogonal. However, normal can also refer to unit vectors. In particular, orthonormal refers to a collection of vectors that are both orthogonal and normal (of unit length). So the orthogonal usage of the term normal is often avoided.
In some contexts, two things are be said to be orthogonal if they are mutually exclusive.
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