cross-product - significado y definición. Qué es cross-product
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Qué (quién) es cross-product - definición

MATHEMATICAL OPERATION ON TWO VECTORS
Vector product; Vector cross product; Evaluating cross products; Cross Product; Evaluating cross-products; Cross products; Sarrus's scheme; Cross-product; Crossproduct; Vector Product; ⨯; Vectorial product; Cross product matrix; Three-dimensional cross product; Ccw test; Xyzzy (mnemonic); Generalizations of the cross product
  • [[Standard basis]] vectors ('''i''', '''j''', '''k''', also denoted '''e'''<sub>1</sub>, '''e'''<sub>2</sub>, '''e'''<sub>3</sub>) and [[vector component]]s of '''a''' ('''a'''<sub>x</sub>, '''a'''<sub>y</sub>, '''a'''<sub>z</sub>, also denoted '''a'''<sub>1</sub>, '''a'''<sub>2</sub>, '''a'''<sub>3</sub>)
  • '''a''' × '''b'''}} (vertical, in purple) changes as the angle between the vectors '''a''' (blue) and '''b''' (red) changes. The cross product is always orthogonal to both vectors, and has magnitude zero when the vectors are parallel and maximum magnitude ‖'''a'''‖‖'''b'''‖ when they are orthogonal.
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  • Figure 1. The area of a parallelogram as the magnitude of a cross product
  • Cross product [[scalar multiplication]]. '''Left:''' Decomposition of '''b''' into components parallel and perpendicular to '''a'''. Right: Scaling of the perpendicular components by a positive real number ''r'' (if negative, '''b''' and the cross product are reversed).
  • rejection]]. The triple product is in the plane and is rotated as shown.
  • The cross product with respect to a right-handed coordinate system
  • The cross product in relation to the exterior product. In red are the orthogonal [[unit vector]], and the "parallel" unit bivector.
  • Figure 2. Three vectors defining a parallelepiped
  • Finding the direction of the cross product by the [[right-hand rule]]
  • According to [[Sarrus's rule]], the [[determinant]] of a 3×3 matrix involves multiplications between matrix elements identified by crossed diagonals

Cross product         
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them.
cross product         
¦ noun another term for vector product.
vector product         
¦ noun Mathematics the product of two vectors which is itself a vector at right angles to both the original vectors and equal to the product of their magnitudes and the sine of the angle between them (written as a . b).

Wikipedia

Cross product

In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E {\displaystyle E} ), and is denoted by the symbol × {\displaystyle \times } . Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b"), is a vector that is perpendicular to both a and b, and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product).

If two vectors have the same direction or have the exact opposite direction from each other (that is, they are not linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths.

The cross product is anticommutative (that is, a × b = − b × a) and is distributive over addition (that is, a × (b + c) = a × b + a × c). The space E {\displaystyle E} together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket.

Like the dot product, it depends on the metric of Euclidean space, but unlike the dot product, it also depends on a choice of orientation (or "handedness") of the space (it's why an oriented space is needed). In connection with the cross product, the exterior product of vectors can be used in arbitrary dimensions (with a bivector or 2-form result) and is independent of the orientation of the space.

The product can be generalized in various ways, using the orientation and metric structure just as for the traditional 3-dimensional cross product, one can, in n dimensions, take the product of n − 1 vectors to produce a vector perpendicular to all of them. But if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions. The cross-product in seven dimensions has undesirable properties, however (e.g. it fails to satisfy the Jacobi identity), so it is not used in mathematical physics to represent quantities such as multi-dimensional space-time. (See § Generalizations, below, for other dimensions.)

Ejemplos de uso de cross-product
1. Prior to joining Nomura Investment Banking in early 2005, he worked for BNP and BNP Paribas in Bahrain from 1''6 where he held a number of roles including responsibility for marketing and product development of equity derivative, cross–product business development for institutional and private clients across the GCC as well as pioneering a range of Shariah–compliant equity derivative products, according to EIIB Managing Director John Weguelin.