SWhat changed
Cayley developed matrix addition, associative noncommutative composition, identity, inverses for nonzero determinant and transpose rules, and extended compatible composition to rectangular matrices. He stated the characteristic equation for arbitrary square order, explicitly demonstrated the two-by-two identity and reported verification in order three, using it to organize matrix powers and low-order examples.
Scientific scope
Cayley developed matrix addition, associative noncommutative composition, identity, inverses for nonzero determinant and transpose rules, and extended compatible composition to rectangular matrices. He stated the characteristic equation for arbitrary square order, explicitly demonstrated the two-by-two identity and reported verification in order three, using it to organize matrix powers and low-order examples. The 1858 memoir explicitly omits a formal proof of the characteristic equation in general order; this entry does not certify that missing proof. Inverses require nonsingularity. Historical claims about all commuting matrices being polynomials in one matrix, and unqualified fractional powers, are not exported as universal valid theorems. No sole-priority claim for all matrix operations or the later Cayley–Hamilton theorem is made.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The 1858 memoir explicitly omits a formal proof of the characteristic equation in general order; this entry does not certify that missing proof. Inverses require nonsingularity. Historical claims about all commuting matrices being polynomials in one matrix, and unqualified fractional powers, are not exported as universal valid theorems. No sole-priority claim for all matrix operations or the later Cayley–Hamilton theorem is made.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.3. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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