Visualizing a projection onto a plane | Linear Algebra | Khan Academy

Visualizing a projection onto a plane. Showing that the old and new definitions of projections aren't that different.

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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

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[Pulsonar]

Wow, superb tutorial, this guy is a natural, learnt more in 10 minutes than I would have done at school in the 80s. I would have turned green and thrown up bile on my desk back in the day.

[muqqebt]

Linear algebra brings calculus and geometry together. The moment that I find out that linear transformation is another form of polynomial transformation, my feet are both in the air and on the ground. Linear transformation was so unreal that it appeared to be cheat and trick, it's truly unbelievable until the connection between linear transformation and polynomial transformation is seen.

[clashcosmos]

"I probably should use different letters instead of using a lowercase and a uppercase v. It makes the language a little difficult."
should have remade the 9min video, 130k people learnt from the confusing variables.

[KnightWhoSaysNi]

Beautifully presented, easily understood. Thank you

[ABIYSCGSTEGD]

This is a good video hampered by lousy graphics. I don't know why professional graphics are not prepared before recording these videos. In this video, it looks like x in the vector space V. I am sure it is meant to be rising from the origin above the plane.