Since we're aiming at data-driven applications, we'll be implementing some of these ideas in code, not just on pencil and paper.

Finally we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. In §7.5, he attempts to address the confusion this caused one student who complained, but I would think it better to bother to use set-builder notation and thus to avoid the problem altogether, as do three of the four freely-available linear algebra textbooks recommended by the American Institute of Mathematics (the one that doesn’t omits null spaces entirely).ĭr Grinfeld, and perhaps his students, likely would make fewer mistakes in Gaussian elimination were he to use augmented matrix notation, as is used in the said three textbooks.In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. §2.12, “Linear Subspaces of the Plane”, is confusing enough that I think it ought to be redone - for now, read the comment under the video.ĭr Grinfeld habitually abuses notation for null spaces, writing a linear combination with unknown coefficients to represent the set of all linear coefficients of its form. I think Dr Grinfeld's linear algebra material is certainly good for its price ($0.00), although my notes from going through the first eight or so chapters note the following small number of issues: There is a website named Lemma run by one Pavel Grinfeld that has a course in linear algebra that is similar to Khan Academy's more developed material, in that it has short lecture videos interspersed with exercises that are graded automatically by the website.

Khan academy algebra linear