= Cayley's matrix memoir
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<Arthur Cayley>'s 1858 paper A Memoir on the Theory of Matrices motivates <matrices> as an abbreviated way to write <systems of linear equations>. Its opening already connects the characteristic equation with reducing <polynomials> in a <matrix> to lower degree. In §21 he works out the two-by-two identity; in §23 he says he has verified the three-by-three case but does not give a formal proof for every size. Thus this source distinguishes the general statement from a general proof.<A Memoir on the Theory of Matrices by Arthur Cayley>[Printed pp. 17–18, opening motivation; pp. 23–24, §§21–25, characteristic equation and reduction of matrix functions; received 10 December 1857, read 14 January 1858, published 1858]{ref} The theorem's name also commemorates <William Rowan Hamilton>.
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