Cayley-Hamilton theorem over a Field
... We look at the set of n equations above, whose coefficients form an n x n matrix. Since F[X] is a Euclidean ring, it is possible by using row operations on that matrix, to change it to an upper-triangular form, for which the corresponding set of n equations is still valid, and such that the determin ...
... We look at the set of n equations above, whose coefficients form an n x n matrix. Since F[X] is a Euclidean ring, it is possible by using row operations on that matrix, to change it to an upper-triangular form, for which the corresponding set of n equations is still valid, and such that the determin ...
10.2
... 2) A Markov Chain is regular if, for some (any) power of the transition matrix P, all entries are positive (no 0's) (Note: if Pn has all positive entries, the every consecutive power of P after that will too) 3) Long term behavior of a regular Markov chain. a) As n gets large, Pn approaches a fixed ...
... 2) A Markov Chain is regular if, for some (any) power of the transition matrix P, all entries are positive (no 0's) (Note: if Pn has all positive entries, the every consecutive power of P after that will too) 3) Long term behavior of a regular Markov chain. a) As n gets large, Pn approaches a fixed ...
