  Peirce was primarily an algebraist in his mathematical style; for example, he was enthusiastic for the cause of quaternions in mechanics after their introduction by W. R. Hamilton in the mid 1840s, and of the various traditions in mechanics he showed some favour for the ‘analytical’ approach, where this adjective refers to the links to algebra. His best remembered publication was a treatment of ‘linear associative algebras’, that is, all algebras in which the associative law x(yz)=(xy)z was upheld. ‘Linear’ did not carry the connotation of matrix theory, which was still being born in others' hands, but referred to the form of linear combination, such as: 