Inverse matrices, column space and null space | Essence of linear algebra, chapter 6
How to think about linear systems of equations geometrically. The focus here is on gaining an intuition for the concepts of inverse matrices, column space, rank ...
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As you can probably tell by now, the bulk of this series is on understanding matrix and vector operations through that more visual lens of linear transformations. This video is no exception, describing the concepts of inverse matrices, column space, rank, and null space through that lens. A forewarning though: I'm not going to talk about the methods for actually computing these things, and some would argue that that's pretty important. There are a lot of very good resources for learning those methods outside this series. Keywords: "Gaussian elimination" and "Row echelon form." I think most of the value that I actually have to add here is on the intuition half. Plus, in practice, we usually get software to compute this stuff for us anyway. First, a few wor...
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As you can probably tell by now, the bulk of this series is on understanding matrix and vector operations through that more visual lens of linear transformations. This video is no exception, describing the concepts of inverse matrices, column space, rank, and null space through that lens. A forewarning though: I'm not going to talk about the methods for actually computing these things, and some would argue that that's pretty important. There are a lot of very good resources for learning those methods outside this series. Keywords: "Gaussian elimination" and "Row echelon form." I think most of the value that I actually have to add here is on the intuition half. Plus, in practice, we usually get software to compute this stuff for us anyway. First, a few wor...
