00 - A New Way to Start Linear Algebra
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MIT A 2020 Vision of Linear Algebra, Spring 2020 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/2020-visionYouTube Playlist: https://www.youtube.com/playlist?list...Professor Strang describes independent vectors and the column space of a matrix as a good starting point for learning linear algebra. His outline develops the five shorthand descriptions of key chapters of linear algebra. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.edu
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GILBERT STRANG: Well, I'm Gil Strang.
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And I'm very happy if you know the linear algebra
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videos on OpenCourseWare or on YouTube.
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That's for the math course 18.06.
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And I'm even happier if you like them.
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And I'm here today to update them for several reasons.
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Well, a lots happened in linear algebra in these years.
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Fortunately, the whole subject has just
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become more and more essential, more and more important, more
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and more beautiful.
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And so I wanted to say something about those later steps.
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And also, when I teach it now, I have a new starting point.
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And I'll show you that.
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So I'll go a little slowly on that starting point.
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The slides tell you the whole course.
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And that's crazy to have a full course within a short video.
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But especially the first part is new.
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And I'm even writing a textbook called
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Linear Algebra for Everyone that will start this way.
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I hope that the new start brings in real linear algebra ideas
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right away.
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And let me show you where those are.
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So this is an outline of the whole video.
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And the first line, which I think
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about in my mind as matrix A, is a product
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of a C matrix, a column matrix, and a row matrix R.
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And you'll see what those are.
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So that's the new idea.
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That will come first.
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Then these are five famous essential shorthand
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descriptions of the key chapters of linear algebra,
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the key chapters.
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So they represent, for example, LU is those letters are famous.
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And computer commands would be exactly
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those letters LU for elimination for solving equations,
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the first job of linear algebra.
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And then QR.
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So Q is a very interesting important type of matrix.
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That's standing for an orthogonal matrix.
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There is the word orthogonal or perpendicular.
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So those are the best matrices to compute with.
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And that QR gets us there.
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And S is for a symmetric matrix.
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And it will involve--
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oh, well, I should say, the first half,
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ending with there, with QR, is about solving equations.
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The second half, these three are about eigenvalues
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and eigenvectors and singular values,
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a different way to approach the whole subject and a very, very
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important way.
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Among my goals is to help courses around the world
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get singular values included because you really
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don't want to miss them.
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That's the high point of the theory.
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And it's expressed like all the others
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as breaking a matrix into two or three pieces, two
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or three parts.
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So that's my plan for this video.
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And I hope it's helpful.
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Again, it's a whole course in a short time.
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And please go to the real 18.06 videos for the details.
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Thanks
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English - CC (English)
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