CP = 
You have not asked this question as if it is a homework assignment, so I'll give an answer.
The characteristic equation GIVEN eigenvalues? Trivial.
The eigenvalues are the roots of a polynomial, known as the characteristic polynomial. What polynomial has roots at a list of points? For example, suppose the eigenvalues are:
EVList = randn(1,5)
What polynomial has those roots?
syms lambda
CP = prod(lambda - EVList)
Feel free to expand it. I'll show only 5 digits, to make it readable.
vpa(expand(CP),5)
You could recover the roots to convince yourself that it worked, but I'll leave that to you.
Can you learn the eigenvalues from a matrix? (HInt: what does eig do?)
What is the characteristic polynomial, given a matrix A?
A = randn(3,3)
CP2 = det(A - lambda*eye(size(A)))
Can we find the roots of that polynomial? You can use solve, or you could extract the coefficients, and then use roots.
solve(CP2)
Are they the same as the eigenvalues, as given by eig?
eig(A)
