The use and properties of Tikhonov filter matrices

We consider the concept of Tikhonov filter matrices in connection with disc rete imposed and rank-deficient linear problems. Important properties of th e Tikhonov filter matrices are given together with their filtering and regu larization effects. We also present new perturbation identities for the Tikhonov regularized li near least squares problem using filter matrices generalizing well-known pe rturbation identities for the linear least squares problem and pseudoinvers es.