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:
““Well then, it’s Granny speaking: ‘I dunnow!
Mebbe I’m wrong to take it as I do.
There ain’t no names quite like the old ones, though,
Nor never will be to my way of thinking.
One mustn’t bear too hard on the newcomers,
But there’s a dite too many of them for comfort....’””
—Robert Frost (1874–1963)
“Watt’s need of semantic succour was at times so great that he would set to trying names on things, and on himself, almost as a woman hats.”
—Samuel Beckett (1906–1989)
“You shall see men you never heard of before, whose names you don’t know,... and many other wild and noble sights before night, such as they who sit in parlors never dream of.”
—Henry David Thoreau (1817–1862)