Transfer matrix

Properties

• .
• If you drop the first and the last column and move the odd-indexed columns to the left and the even-indexed columns to the right, then you obtain a transposed Sylvester matrix.
• The determinant of a transfer matrix is essentially a resultant.
• For the trace of the transfer matrix of convolved masks holds
• For the determinant of the transfer matrix of convolved mask holds
• If, then.
• If is an eigenvector of with respect to the eigenvalue, i.e.
• Let be the eigenvalues of, which implies and more generally. This sum is useful for estimating the spectral radius of. There is an alternative possibility for computing the sum of eigenvalue powers, which is faster for small.
• From the previous statement we can derive an estimate of the spectral radius of. It holds