Have not watched the videos yet, but that seems to me more like an 1820 vision of linear algebra :-)
If you look at the order of topics in his book "An Introduction to Linear Algebra", you will find the topic "Linear Transformation" way back in chapter 8! Even after the chapters eigenvalue decomposition and singular value decomposition. But understanding that a matrix is just the representation of a linear transformation in a particular basis is probably the most important and first thing you should learn about matrices ...
If you look at the order of topics in his book "An Introduction to Linear Algebra", you will find the topic "Linear Transformation" way back in chapter 8! Even after the chapters eigenvalue decomposition and singular value decomposition. But understanding that a matrix is just the representation of a linear transformation in a particular basis is probably the most important and first thing you should learn about matrices ...