Names
The cross product is also called the vector product or Gibbs' vector product. The name Gibbs' vector product is after Josiah Willard Gibbs, who around 1881 introduced both the dot product and the cross product, using a dot (a · b) and a cross (a × b) to denote them.
To emphasize the fact that the result of a dot product is a scalar, while the result of a cross product is a vector, Gibbs also introduced the alternative names scalar product and vector product for the two operations. These alternative names are still widely used in the literature.
Both the cross notation (a × b) and the name cross product were possibly inspired by the fact that each scalar component of a × b is computed by multiplying non-corresponding components of a and b. Conversely, a dot product a · b involves multiplications between corresponding components of a and b. As explained below, the cross product can be defined as the determinant of a special 3×3 matrix. According to Sarrus' rule, this involves multiplications between matrix elements identified by crossed diagonals.
Read more about this topic: Cross Product
Famous quotes containing the word names:
“I introduced her to Elena, and in that life-quickening atmosphere of a big railway station where everything is something trembling on the brink of something else, thus to be clutched and cherished, the exchange of a few words was enough to enable two totally dissimilar women to start calling each other by their pet names the very next time they met.”
—Vladimir Nabokov (1899–1977)
“Being the dependents of the general government, and looking to its treasury as the source of all their emoluments, the state officers, under whatever names they might pass and by whatever forms their duties might be prescribed, would in effect be the mere stipendiaries and instruments of the central power.”
—Andrew Jackson (1767–1845)
“Men have sometimes exchanged names with their friends, as if they would signify that in their friend each loved his own soul.”
—Ralph Waldo Emerson (1803–1882)