MATH1002 Lecture Notes - Lecture 12: Markov Chain, Stochastic Matrix, Row And Column Vectors

• School: University of Sydney
• Department: Mathematics
• Course: MATH1002
• Professor: Nathan Brownlowe

Document Summary

F average # of female offspring produced by a female in age class i. S the probability that a female in one age class i survives to the next age i i class. We are generally given initial conditions in the form of a column vector x with distribution of females among age classes. M age classes are spanned x= lmx m. Let a be a n x n matrix. A non-zero vector in rnis an eigenvector if there exists a scalar in r such that av = v. All eigenvectors in rnare a subspace of rn. Eigenspace is the same as the null space of (a- i) Is an eigenvalue of a if null(a- i) [0] Using this theorem, we can find the determinant, knowing it is 0, and find both eigenvalues of the system. The determinant gives us the characteristic polynomial, which we solve for the eigenvalues.