A stochastic matrix is a matrix whose entries are nonnegative, and where the entries in any given column add to 1. Among other things, they are used for modeling internet traffic. Let M be a stochastic matrix. Explain why M and MT have the same eigenvalues. Suggestion: Since you're not actually trying to find the eigenvalues, consider the characteristic polynomial. Edit Insert Formats B I U X, X ' = = : =- @ Find an eigenvector for MT. Suggestion: Remember the entries of the columns of M add to 1. This means the entries of each row of MT add to 1. Edit Insert Formats BI I U x x A A = = = : GJ & + What is the corresponding eigenvalue? Edit Insert Formats BIU X X = = = EVE E A + A O + Given a matrix M, a steady state vector v is a vector that satisfies Mv = v. Explain why your work above proves that stochastic matrices always have steady state vectors.