Question

finding characteristic equation of linear homogenous recurrence relation

Answer 1

Linear homogeneous recurrences
A linear homogenous recurrence relation of degree k with
constant coefficients is a recurrence relation of the form
an = c1an-1 + c2an-2 + … + ckan-k,
where c1, c2, …, ck are real numbers, and ck0.
an is expressed in terms of the previous k terms of the sequence,
so its degree is k.
This recurrence includes k initial conditions.
a0 = C0 a1 = C1 … ak = Ck

Answer 2

Hey User______✌✌_________
_________________________________________________________________________________Given a second-order linear homogeneous recurrence relation with constant coefficients, if the character- istic equation has two distinct roots, then Lemmas 1 and 2 can be used tofind an explicit formula for any sequence that satisfies a second-orderlinear homogeneous recurrence relation with constant coefficients ..


The equation det (M - xI) = 0 is a polynomial equation in the variable x for given M. It is called the characteristic equation of the matrix M. You can solve it to find the eigenvalues x, of M. The trace of a square matrix M, written as Tr(M), is the sum of its diagonal elements.
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