Cayley–Hamilton theorem
Teorema de Cayley-Hamilton
- Date
- 1858 · confidence medium
- Place
- London, England, United Kingdom
- Credited to
- Arthur Cayley (with earlier cases by William Rowan Hamilton)
- Field
- Knowledge & symbols
What was discovered
While practicing law in London, Cayley stated that every square matrix satisfies its own characteristic equation, though he only published a proof for 2×2 matrices. The general result links matrix algebra to characteristic polynomials.
Hamilton had proved a special case for quaternions in 1853 (Dublin); Cayley stated the general case in 1858 in London but only proved the 2×2 case; Ferdinand Frobenius gave the first general proof in 1878 in Berlin.
What it led to
- Computation of matrix functions
- Applications in linear algebra and algebraic number theory
- Frobenius's general proof in 1878