Who developed the theory of matrices in an 1858 memoir and had introduced the now-standard vertical-line notation for determinants in 1841?

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Arthur Cayley

Arthur Cayley is often considered the founder of matrix theory, as he was the first to treat matrices as single algebraic entities that could be added and multiplied. His 1858 "Memoir on the Theory of Matrices" introduced these fundamental concepts, while his earlier work established the vertical-line notation we still use for determinants today. Remarkably, Cayley balanced his mathematical genius with a full-time career as a lawyer for nearly three decades.

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