search for: lambda_n

Hi, Given a positive integer N, and a real number \lambda such that 0 < \lambda < 1, I would like to generate an N by N stochastic matrix (a matrix with all the rows summing to 1), such that it has the second largest eigenvalue equal to \lambda (Note: the dominant eigenvalue of a stochastic matrix is 1). I don't care what the other eigenvalues are. The second eigenvalue is

Hi, If I set df=2 in my smooth.spline function, is that equivalent to running a linear regression through my data? It appears that df=# of data points gives the interpolating spline and that df = 2 gives the linear regression, but I just want to confirm this. Thank you, Steven