An nxn matrix A n = (a i} ) is tri-diagonal if a i} = 0 for | i-j | ^ 2. The latent roots of such matrices may be conveniently studied by forming the sequence of polynomials ^(A) = | XI-A k \, where A k is the principal submatrix of A k+1 obtained by deleting the last row and column of A k+1 , and then observing that these polynomials satisfy the following recurrence relation: «F o tt) = 1, ^(A) = X-a llt k = 1,2, .