Definitions for bivector
bivec·tor

WiktionaryRate this definition:0.0 / 0 votes

1. bivectornoun

   An antisymmetric tensor of second rank

WikipediaRate this definition:0.0 / 0 votes

1. Bivector

   In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. If a scalar is considered a degree-zero quantity, and a vector is a degree-one quantity, then a bivector can be thought of as being of degree two. Bivectors have applications in many areas of mathematics and physics. They are related to complex numbers in two dimensions and to both pseudovectors and quaternions in three dimensions. They can be used to generate rotations in any number of dimensions, and are a useful tool for classifying such rotations. They are also used in physics, tying together a number of otherwise unrelated quantities. Bivectors are generated by the exterior product on vectors: given two vectors a and b, their exterior product a ∧ b is a bivector, as is the sum of any bivectors. Not all bivectors can be generated as a single exterior product. More precisely, a bivector that can be expressed as an exterior product is called simple; in up to three dimensions all bivectors are simple, but in higher dimensions this is not the case. The exterior product of two vectors is alternating, so b ∧ a is the negation of the bivector a ∧ b, producing the opposite orientation, and a ∧ a is the zero bivector. Geometrically, a simple bivector can be interpreted as an oriented plane segment, much as vectors can be thought of as directed line segments. The bivector a ∧ b has a magnitude equal to the area of the parallelogram with edges a and b, has the attitude of the plane spanned by a and b, and has orientation being the sense of the rotation that would align a with b.In layman terms, any surface is the same bivector, if it has the same area, same orientation, and is parallel to the same plane (see figure).

Webster DictionaryRate this definition:0.0 / 0 votes

1. Bivectornoun

   a term made up of the two parts / + /1 /-1, where / and /1 are vectors

WikidataRate this definition:0.0 / 0 votes

1. Bivector

   In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. If a scalar is considered an order zero quantity, and a vector is an order one quantity, then a bivector can be thought of as being of order two. Bivectors have applications in many areas of mathematics and physics. They are related to complex numbers in two dimensions and to both pseudovectors and quaternions in three dimensions. They can be used to generate rotations in any dimension, and are a useful tool for classifying such rotations. They also are used in physics, tying together a number of otherwise unrelated quantities. Bivectors are generated by the exterior product on vectors: given two vectors a and b, their exterior product a ∧ b is a bivector, as is the sum of any bivectors. Not all bivectors can be generated as a single exterior product. More precisely, a bivector that can be expressed as an exterior product is called simple; in up to three dimensions all bivectors are simple, but in higher dimensions this is not the case. The exterior product is antisymmetric, so b ∧ a is the negation of the bivector a ∧ b, producing the opposite orientation, and a ∧ a is the zero bivector.

How to pronounce bivector?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say bivector in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of bivector in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of bivector in Pythagorean Numerology is: 4

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Bivector
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Bivector
3. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/bivector
4. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=bivector