Cross Product
In mathematics, the cross product, vector product, or Gibbs' vector product is a binary operation on two vectors in three-dimensional space. It results in a vector which is perpendicular to both of the vectors being multiplied and therefore normal to the plane containing them. It has many applications in mathematics, physics, and engineering.
Read more about Cross Product.
Some articles on cross product:
... The cross product is a product in vector algebra ... Cross product may also refer to Seven-dimensional cross product, a related product in seven dimensions A product in a Künneth theorem A crossed product in von Neumann algebras A Cartesian ...
... In three dimensions the cross product is invariant under the group of the rotation group, SO(3), so the cross product of x and y after they are rotated is the image of x × y under the rotation ... But this invariance is not true in seven dimensions that is, the cross product is not invariant under the group of rotations in seven dimensions, SO(7) ...
... in some right-handed coordinate system using an orthonormal basis), their cross product can be written as a determinant hence also using the Levi-Civita symbol, and more simply In Einstein notation ...
... To define a particular cross product, an orthonormal basis {ej} may be selected and a multiplication table provided that determines all the products {ei × ej} ... to five other unit vectors, allowing many choices for each cross product ... table from the one in the Introduction, leading to a different cross product, is given with anticommutativity by More compactly this rule can be written as with i = 1...7 modulo 7 and the indices i, i + 1 and i + 3 ...
... Lagrange introduced the component form of both the dot and cross products in order to study the tetrahedron in three dimensions ... In 1843 the Irish mathematical physicist Sir William Rowan Hamilton introduced the quaternion product, and with it the terms "vector" and "scalar" ... u and v are vectors in R3, their quaternion product can be summarized as ...
Famous quotes containing the words product and/or cross:
“Labor is work that leaves no trace behind it when it is finished, or if it does, as in the case of the tilled field, this product of human activity requires still more labor, incessant, tireless labor, to maintain its identity as a “work” of man.”
—Mary McCarthy (1912–1989)
“We are no longer in a state of growth; we are in a state of excess. We are living in a society of excrescence.... The boil is growing out of control, recklessly at cross purposes with itself, its impacts multiplying as the causes disintegrate.”
—Jean Baudrillard (b. 1929)