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.