Left Inverse

This part needs to be filled, but first things that I may forget later.

If $$BA = I$$, then the matrix $$B$$ is the left inverse of $$A$$. Clearly, if $$y=Ax$$, then $$By = BAx = x$$.

In the context of encoding, $$B$$ is called the perfect decoder. In the context of communication system, $$B$$ is the perfect equalizer. In the context of a measurement system, $$B$$ is the matrix that gives the parameters that we wanted to measure.