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:
“The world is a puzzling place today. All these banks sending us credit cards, with our names on them. Well, we didn’t order any credit cards! We don’t spend what we don’t have. So we just cut them in half and throw them out, just as soon as we open them in the mail. Imagine a bank sending credit cards to two ladies over a hundred years old! What are those folks thinking?”
—Sarah Louise Delany (b. 1889)
“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)
“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)