Every square matrix satisfies its own characteristic polynomial. Named for Arthur Cayley and William Rowan Hamilton, it is a basic structural fact of linear algebra with wide use in matrix computation.
Facts
StatementThe Cayley-Hamilton theorem states that every square matrix over a commutative ring satisfies its own characteristic equation. 1 Classification
Statement Form Cayley-Hamilton Theorem
Filter Results1 entry
Connections
Has Statement Form
In Branch
Principal Result Of
Source Cayley-Hamilton Theorem (Wikipedia)
Proved By
Sources
1. Cayley-Hamilton Theorem (Wikipedia)
Wikimedia FoundationLead section, opening sentence
In linear algebra, the Cayley-Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies its own characteristic equation.
History section, on Frobenius's general proof
The general case was first proved by Ferdinand Frobenius in 1878.
In Group: Linear Algebra and Matrix Theory, Lead section
In linear algebra, the Cayley-Hamilton theorem (named after the
View the Source Cayley-Hamilton Theorem (Wikipedia)
Principal Result Of: William Rowan Hamilton, Lead sentence of the article on the resultQuote, Principal Result Of: William Rowan Hamilton, Lead sentence of the article on the result
In linear algebra, the Cayley-Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies its own characteristic equation.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.