well I'm Gil Strang and I'm very happy if you know the linear algebra videos on OpenCourseWare or on YouTube that's for the math course 1806 and I've even happier if you like them and here today to update them for several reasons well lots happened a lot has happened in linear algebra in these years fortunately the whole subject has just become more and more essential more and more important more more beautiful and so I wanted to say something about the those later steps and also when I teach it now I have a new starting point and I'll show you that so I'll go a little slowly on that starting point this the slides tell you the whole course and that's like crazy to have a full course within the short video but especially the first part is new and and I'm even writing a textbook called linear algebra for everyone that will start this way I hope that the new start brings in sort of real linear algebra ideas write it right away and let me show you where those are so this is an outline of the whole video and the first line which I think about in my mind as a matrix a is the product of a C matrix a column matrix and a row matrix R and you'll see what those are so that's the new idea that when that will come first then these are five famous essential shorthand descriptions of the key chapters of linear algebra the key chapter so they represent for example Lu is those letters are famous and and computer commands would be actually those letters lu4 elimination for solving equations the first job of the linear algebra and then QR so Q is a very interesting important type of matrix that's standing for an orthogonal matrix there's the word orthogonal or perpendicular so those are the best matrices to compute with and that QR is gets us there and s is for a symmetric matrix and it will involve oh well I should say the first half ending with there with QR is about solving equations the second half the these three are about eigenvalues and eigenvectors and singular values a different way to approach the whole subject and a very very important way among my goals is to help courses around the world get singular values included because you really don't want to miss them there the that's a high point of of the theory and it's expressed like all the others as a as a breaking a matrix into two or three pieces two or three parts so that's my plan for this video and I hope it's helpful again it's a whole course in a short time and please go to the real 1806 videos for the details thanks