 James Joseph Sylvester

James Joseph Sylvester was a mathematician whose work with Arthur Cayley helped develop linear algebra and invariant theory. He studied algebraic forms, their relations and quantities that detect special behavior of polynomials; his terminology included the discriminant.^[ref] His Sylvester's law of inertia explains why the numbers of positive and negative squares in a real quadratic form are unchanged by an invertible linear change of variables. Thus matrices that look different can describe the same underlying geometry, and the signs provide invariants that survive a change of coordinates.

Identity source: mathshistory.st-andrews.ac.uk/Biographies/Sylvester/

James Joseph Sylvester (1814–1897) was a prominent English mathematician known for his contributions to various fields, including algebra, matrix theory, and number theory. He played a pivotal role in the development of invariant theory and is credited with the introduction of several important concepts, such as Sylvester's law of inertia and the Sylvester matrix. Sylvester was also known for his work on determinants and his role in the early formation of the theory of linear transformations.