A projection onto a subspace is a linear transformation | Linear Algebra | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacademy.org/math/line...
Showing that a projection onto a subspace is a linear transformation
Watch the next lesson: www.khanacademy.org/math/line...
Missed the previous lesson?
www.khanacademy.org/math/line...
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.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel: / channel
Subscribe to KhanAcademy: kzbin.info_...

[@zeyadzakaria5223]

yeah, the video has been here for 13 years and yet it is still helpful, thank you.

[@ateebahmed2237]

Excellent.. Far better than Gilbert strang on this topic. Thanks sal k-han

[@tung-hsinliu861]

This is the closest time I am able to understand matrix projection. Very appreciated!

[@debendragurung3033]

9:30, use of left null space algebraically. Never thought of that..

[@monsieuralexandergulbu3678]

That's amazing, thank you very much!

[@user-mu2qq3eb7t]

This is beautiful! I'm beginning to see the magic of the Matrix. LOL. Thanks a lot!

[@norwayte]

The last minute saved it.

[@Arcel4]

Excellent !

[@bewarethebeef1]

awesome

[@debendragurung3033]

is the Matrix A in here considered as the nullspace of some other transformation. Is this some sort of Null Space of a Nullspace thing. help me I'm lost

[@bingjieshi5578]

字幕又错了 product不是点积！

[@Diana-yl1jo]

这集看的一脸懵逼