In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix...

Cambridge for 35 years. He postulated what is now known as the Cayley–Hamilton theorem—that every square matrix is a root of its own characteristic polynomial...

R[s,t].} Multiply sI − A by its adjugate. Since p(A) = 0 by the Cayley–Hamilton theorem, some elementary manipulations reveal adj ⁡ ( s I − A ) = Δ p (...

clearly the characteristic polynomial of the Jordan form of A. The Cayley–Hamilton theorem asserts that every matrix A satisfies its characteristic equation:...

Cayley graph of a finite Coxeter group is Hamiltonian (For more information on Hamiltonian paths in Cayley graphs, see the Lovász conjecture.) Cayley...

{tr} A^{k-1}&&\cdots &\operatorname {tr} A\end{vmatrix}}~.} The Cayley–Hamilton theorem states that replacing t {\displaystyle t} by A {\displaystyle A}...

main ingredients for the following proof are the Cayley–Hamilton theorem and the fundamental theorem of algebra. Let D be the division algebra in question...

Hamilton's principle, Hamilton's principal function, the Hamilton–Jacobi equation, Cayley-Hamilton theorem are named after Hamilton. The Hamiltonian is...

known as Padé approximants), and gave the first full proof for the Cayley–Hamilton theorem. He also lent his name to certain differential-geometric objects...

equation, as its roots are exactly the eigenvalues of A. By the Cayley–Hamilton theorem, A itself obeys the same equation: pA(A) = 0. As a consequence...

Many theorems were first established for small matrices only, for example, the Cayley–Hamilton theorem was proved for 2×2 matrices by Cayley in the...

matrix. Cartan matrix Cayley-Hamilton theorem Brown 1991, Definition I.2.28 Brown 1991, Definition I.5.13 Horn & Johnson 1985, Theorem 2.5.6 Horn & Johnson 1985...

a matrix polynomial in the matrix A itself, it vanishes by the Cayley–Hamilton theorem. Computing the characteristic polynomial directly from the definition...

contaminated by small errors from imperfect computer arithmetic. The Cayley–Hamilton theorem allows the inverse of A to be expressed in terms of det(A), traces...

the lemma is a simple consequence of a generalized form of the Cayley–Hamilton theorem, an observation made by Michael Atiyah (1969). The special case...

A ) = 0 {\displaystyle p(A)=0} due to the Cayley–Hamilton theorem; meanwhile, the spectral mapping theorem tells us σ ( p ( − B ) ) = p ( σ ( − B ) )...

after William Rowan Hamilton: Cayley–Hamilton theorem Hamilton's equations Hamilton's principle Hamilton–Jacobi equation Hamilton–Jacobi–Bellman equation...

(A)-6\operatorname {tr} \left(A^{4}\right)\right).\end{aligned}}} cf. Cayley-Hamilton theorem. Such expressions are deducible from combinatorial arguments, Newton's...

{\pi }{6}}\right)^{12}&=N+P=I\\\end{aligned}}} By virtue of the Cayley–Hamilton theorem the matrix exponential is expressible as a polynomial of order...

Cayley graph Cayley numbers Cayley plane Cayley table Cayley transform Cayleyan Cayley–Bacharach theorem Cayley–Dickson construction Cayley–Hamilton theorem...

algebra) Cayley–Hamilton theorem (Linear algebra) Dimension theorem for vector spaces (vector spaces, linear algebra) Euler's rotation theorem (geometry)...

matrices are nilpotent of index at most n as a consequence of the Cayley-Hamilton theorem. An atomic (lower or upper) triangular matrix is a special form...

polynomial is the multiple of the minimal polynomial of an operator A. Cayley–Hamilton theorem Minimal polynomial (linear algebra) Taboga, Marco. "Minimal Polynomial"...

characteristic polynomial, which is one way of formulating the Cayley–Hamilton theorem (for the case of matrices over a field). Given an endomorphism...

linear transformations represented as matrices, most notably the Cayley–Hamilton theorem. The characteristic polynomial of a matrix A is a scalar-valued...

n × 1 {\displaystyle n\times 1} constant vector. By use of the Cayley–Hamilton theorem and Vandermonde-type matrices, this formal matrix exponential solution...

n-set.) Straubing, Howard (1983), "A combinatorial proof of the Cayley-Hamilton theorem", Discrete Mathematics, 43 (2–3): 273–279, doi:10.1016/0012-365X(83)90164-4...

Characteristic polynomial Trace Eigenvalue, eigenvector and eigenspace Cayley–Hamilton theorem Spread of a matrix Jordan normal form Weyr canonical form Rank...

matrix has a minimal polynomial (not necessarily irreducible). By Cayley–Hamilton theorem, the evaluation homomorphism maps to zero the characteristic polynomial...

represents an element x has integer entries in some basis e. By the Cayley–Hamilton theorem, pA(A) = 0, and it follows that pA(x) = 0, so that x is an algebraic...