A Memoir on the Theory of Matrices

Cayley, A. (1858). A Memoir on the Theory of Matrices. Philosophical Transactions of the Royal Society of London, 17-37.

Type

Journal article

Intellectual base

Primary research

Year

1858

DOI

10.1098/rstl.1858.0002

Link

https://doi.org/10.1098/rstl.1858.0002

Cited from

mathematics

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Associativity
  • (2) associativity is a property of a specific operation, independent of commutativity — many important operations are associative without being commutative, including function composition, matrix multiplication (Cayley 1858 established matrix algebra as an associative operation under multiplication)

    This sourceFounds the theory of matrices

• Commutativity
  • … unavailable in non-commutative settings; (2) commutativity is a property of a specific operation on a specific structure, not a property of a set alone — addition and multiplication of integers are commutative, but subtraction and division are not; matrix multiplication is non-commutative (in general $AB \neq BA$)

    This sourceFirst systematic paper on matrix algebra; establishes matrix multiplication as an associative but (in general) non-commutative operation — supports both the AB ≠ BA claim and the associative-non-commutative claim.

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