The Theory of Determinants, Matrices and Invariants

THIS excellent book gives a survey of a field which has come into great prominence during the present century for two quite different reasons. First, the theory of relativity has compelled physicists to extend their notions of space with the consequent necessity for formulating physical invariants appertaining to quaternary and higher forms. Secondly, the new mechanics has found a need for numbers obeying a non-commutative law of multiplication. Here the matrix representation was ready to hand. Prof. Turnbull has not made the mistake of attempting to develop the theory with an eye to its applications. Rather he has given a consistent and adequate account from the point of view of pure mathematics. Seven chapters on determinants and matrices are followed by a development of invariant theory mainly of quaternary and higher forms. Naturally in a subject of such vast extent a choice has to be made, but it will be found that the choice is extremely judicious.The Theory of Determinants, Matrices and Invariants.By Prof. H. W. Turnbull. Pp. xvi + 338. (London and Glasgow: Blackie and Son, Ltd., 1928.) 25s. net.