Cayley-Hamilton theorem

Cayley-Hamilton theorem

[¦kāl·ē ¦ham·əl·tən ‚thir·əm]
(mathematics)
The theorem that a linear transformation or matrix is a root of its own characteristic polynomial. Also known as Hamilton-Cayley theorem.
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The topics include Kyiv from the fall of 1943 through 1946: the rebirth of mathematics, two consequences of extension of local maps of Banach spaces: applications and examples, Hasse-Schmidt derivations and the Cayley-Hamilton theorem for exterior algebras, some binomial formulae for non-commuting operators, and the complete metric space of Riemann integrable functions and differential calculus in it.
However, if n is a noninteger, then we need to revert to the Cayley-Hamilton theorem. In particular, if M is a 2 x 2 matrix and I is an identify matrix, then
Then q(z) is a monic polynomial of degree m such that, by the Cayley-Hamilton theorem, q(T) = 0.
We will use the well-known Cayley-Hamilton theorem to find the form of the matrix
Using Cayley-Hamilton theorem, we can express [A.sup.2] and higher powers of the matrix A in terms of I and A, where I is the unit matrix of the second order.
We know from Cayley-Hamilton theorem that [A.sup.r] = [[gamma].sub.1] A + [[gamma].sub.0] I.
(2) If n is even (nothing to do) as this is Cayley-Hamilton theorem
They proceed to a combinatorial argument for the classical Cayley-Hamilton theorem and describe non-negative matrices and their special properties.