The core object in linear algebra is a linear map, that translates one vector space to another while satisfying certain properties, as described in chapter-1.
In this chapter, we’ll introduce the important concept of the rank of a matrix/ linear map. It is a single number (integer) that encodes important information about the corresponding objects. Note that the determinant (chapter 2) had a similar role. And indeed, the two complement each other, with the rank providing further granularity for cases where the determinant looks the same.