A Bird’s-Eye View of Linear Algebra: Rank-Nullity and Why Row Rank Equals Column Rank

The core object in linear algebra is a linear map, that translates one vector space to another while satisfying certain properties, as described in <a href="https://medium.com/towards-data-science/a-birds-eye-view-of-linear-algebra-the-basics-29ad2122d98f" rel="noopener">chapter-1</a>. 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 (<a href="https://towardsdatascience.com/a-birds-eye-view-of-linear-algebra-the-measure-of-a-map-determinant-1e5fd752a3be" rel="noopener" target="_blank">chapter 2</a>) 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. <a href="https://towardsdatascience.com/a-birds-eye-view-of-linear-algebra-rank-nullity-and-why-row-rank-equals-column-rank-bc084e0e1075">Click Here</a>