  A unified linear algebraic approach to adaptive signal processing (ASP) is
presented. Starting from just Ax=b, key ASP algorithms are derived in a simple,
systematic, and integrated manner without requiring any background knowledge to
the field. Algorithms covered are Steepest Descent, LMS, Normalized LMS,
Kaczmarz, Affine Projection, RLS, Kalman filter, and MMSE/Least Square Wiener
filters. By following this approach, readers will discover a synthesis; they
will learn that one and only one equation is involved in all these algorithms.
They will also learn that this one equation forms the basis of more advanced
algorithms like reduced rank adaptive filters, extended Kalman filter, particle
filters, multigrid methods, preconditioning methods, Krylov subspace methods
and conjugate gradients. This will enable them to enter many sophisticated
realms of modern research and development. Eventually, this one equation will
not only become their passport to ASP but also to many highly specialized areas
of computational science and engineering.
