CAYLEY-HAMILTON THEORUM & MATRICES: "Memoir on the Theory of Matrices" & "A Memoir on the Automorphic Linear Transformation of Bipartite Quadric Function" (Philosophical Transactions of the Royal Society of London, Vol. 148 for the Year 1858, pp. 17-37, 39-52).
London: Royal Society of London, 1858. Hardcover. First Edition. v, , 21, -909 pp. 4to. Library binding, tan leather spine with gold embossed titling. Interiors clean, ex-library stamp on title page, and occurring sporadically within. Numerous folding plates that illustrate articles. Pages were trimmed slightly when rebound. Very Good.
Arthur Cayley (1821-1895) introduces matrices to simplify the notation which arises in simultaneous linear equations. He further introduces the ideas of unit matrix, matrix addition and multiplication, inverse matrix and powers of matrices. More significantly, Cayley introduces the algebraic notation of matrix calculus, explores the non-commutative algebra associated with matrix multiplication and proves the Cayley-Hamilton Theorem that every matrix satisfies its own characteristic equation.
Also contains John P. Gassiot's "The Bakerian Lecture -- On the Stratifications and Dark Band in Electrical Discharges as observed in Torricellian Vacua" (Volume 148 pp. 1-16, 1858) and Joseph Lister's "An Inquiry Regarding the Parts of the Nervous System Which Regulate the Contractions of the Arteries," "On the Cutaneous Pigmentary System of the Frog," & "On the Early Stages of Inflammation" (pp. 607-625, 627-643, 645-702).