An introduction to S-Bases in S-Linear Algebra

In this lecture note we define the S-bases for the spaces of tempered distributions. These new bases are the analogous of Hilbert bases of separable Hilbert spaces for the continuous case (they are indexed by m-dimensional Euclidean spaces) and enjoy properties similar to those shown by algebraic bases in the finite dimensional case. The S-bases are one possible rigorous and extremely manageable mathematical model for the "physical" bases used in Quantum Mechanics.