What does sesquilinear mean?
Definitions for sesquilinear
sesquilin·ear
This dictionary definitions page includes all the possible meanings, example usage and translations of the word sesquilinear.
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Wiktionary
sesquilinearadjective
Linear in one coordinate and conjugate linear in the other
Etymology: ; “conjugate linear” being considered metaphorically “half linear”, hence one and a half times linear, as opposed to bilinear.
Wikipedia
sesquilinear
In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space. A bilinear form is linear in each of its arguments, but a sesquilinear form allows one of the arguments to be "twisted" in a semilinear manner, thus the name; which originates from the Latin numerical prefix sesqui- meaning "one and a half". The basic concept of the dot product – producing a scalar from a pair of vectors – can be generalized by allowing a broader range of scalar values and, perhaps simultaneously, by widening the definition of a vector. A motivating special case is a sesquilinear form on a complex vector space, V. This is a map V × V → C that is linear in one argument and "twists" the linearity of the other argument by complex conjugation (referred to as being antilinear in the other argument). This case arises naturally in mathematical physics applications. Another important case allows the scalars to come from any field and the twist is provided by a field automorphism. An application in projective geometry requires that the scalars come from a division ring (skew field), K, and this means that the "vectors" should be replaced by elements of a K-module. In a very general setting, sesquilinear forms can be defined over R-modules for arbitrary rings R.
Numerology
Chaldean Numerology
The numerical value of sesquilinear in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of sesquilinear in Pythagorean Numerology is: 5
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"sesquilinear." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/sesquilinear>.
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