Whyte notation
The Whyte notation for classifying steam locomotives by wheel arrangement was devised by Frederick Methvan Whyte, and came into use in the early twentieth century following a December 1900 editorial in "American Engineer and Railroad Journal". The notation counts the number of leading wheels, then the number of driving wheels, and finally the number of trailing wheels, groups of numbers being separated by dashes. Other classification schemes, like UIC classification and the French, Turkish and Swiss systems for steam locomotives, count axles rather than wheels.
History of mathematical notation
Matrix notation would be more fully developed by Arthur Cayley in his three papers, on subjects which had been suggested by reading the Mécanique analytique of Lagrange and some of the works of Laplace. Cayley defined matrix multiplication and matrix inverses. Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote ""There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants"".
William Rowan Hamilton would introduce the nabla symbol for vector differentials. This was previously used by Hamilton as a general-purpose operator sign. Hamilton reformulated Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism. This was also important to the development of quantum mechanics. In mathematics, he is perhaps best known as the inventor of quaternion notation and biquaternions. Hamilton also introduced the word "tensor" in 1846. James Cockle would develop the tessarines and, in 1849, coquaternions. In 1848, James Joseph Sylvester introduced into matrix algebra the term matrix.