Ορθογωνιότης
- Μία ιδιότητα.
Ετυμολογία[]
Η ονομασία "Ορθογωνιότητα" σχετίζεται ετυμολογικά με την λέξη "γωνία".
Εισαγωγή[]
- In geometry, two Euclidean vectors are orthogonal if they are perpendicular, i.e., they form a right angle.
- Two vectors, x and y, in an inner product space, V, are orthogonal if their inner product is zero.[1] This relationship is denoted .
- Two vector subspaces, A and B, of an inner product space V, are called orthogonal subspaces if each vector in A is orthogonal to each vector in B. The largest subspace of V that is orthogonal to a given subspace is its orthogonal complement.
- Given a module M and its dual M∗, an element m′ of M∗ and an element m of M are orthogonal if their natural pairing is zero, i.e. Πρότυπο:Langlem′, mΠρότυπο:Rangle = 0. Two sets S′ ⊆ M∗ and S ⊆ M are orthogonal if each element of S′ is orthogonal to each element of S.[2]
- A term rewriting system is said to be orthogonal if it is left-linear and is non-ambiguous. Orthogonal term rewriting systems are confluent.
A set of vectors in an inner product space is called pairwise orthogonal if each pairing of them is orthogonal. Such a set is called an orthogonal set.
In certain cases, the word normal is used to mean orthogonal, particularly in the geometric sense as in the normal to a surface. For example, the y-axis is normal to the curve y = x2 at the origin. However, normal may also refer to the magnitude of a vector. In particular, a set is called orthonormal (orthogonal plus normal) if it is an orthogonal set of unit vectors. As a result, use of the term normal to mean "orthogonal" is often avoided. The word "normal" also has a different meaning in probability and statistics.
A vector space with a bilinear form generalizes the case of an inner product. When the bilinear form applied to two vectors results in zero, then they are orthogonal. The case of a pseudo-Euclidean plane uses the term hyperbolic orthogonality. In the diagram, axes x′ and t′ are hyperbolic-orthogonal for any given ϕ.
Υποσημειώσεις[]
- ↑ Wolfram MathWorld. http://mathworld.wolfram.com/Orthogonal.html.
- ↑ Bourbaki, Algebra I, σελ. 234
Εσωτερική Αρθρογραφία[]
Βιβλιογραφία[]
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