Alternate basis transformation matrix example | Linear Algebra | Khan Academy

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Example of finding the transformation matrix for an alternate basis
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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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[@wonderpope]

this reminds me of what my algebra professor used to say: linear algebra is the art of choosing the right basis

[@rdsaz]

at 7:30, did you mean to write [T(x)]b instead of T([x]b)? Because I think setting T([x]b) equal to D[x]b just makes A=D, right? If not, I'm really confused. Thanks

[@AvivAtias]

@alkalait Sal's linear algebra playlist is truly a marvelous thriller!

[@beckyw24]

thankyou sooooo much for these videos! saved my life ;)

[@kyungwonpark6506]

I have a question. Given the diagram earlier in this video, why isn't D equal to C * A * C inverse? why is it the opposite order?

[@woosterjeeves]

To go from [X]b to [Tx]b, trace the lines. From [X]b up to X, we do C. Then from X to T(x), we do A. Then from T(x) to [Tx]b we do Cinv. So the entire journey is first C, then A, then C.inv applied sequentially to [x]b. Hence Cinv* A*C* [x]b gives [Tx]b. Hope this helps.

[@lawfordcodner3507]

Can you make some 3 variables linear equations word problems in investment, finance and mixtures thank you.

[@mrspeckter]

6:08 please start from there always xD I like concrete examples!

[@4741438]

ur a god

[@Anonymous-yb4yh]

thankuuuuuuuuuuuuuuuuuuu

[@CANN1BLE1]

Hey Sal Khan, have you ever heard of the black pigeon. He has a youtube channel under that name, and you sound practically identical to one another. You wouldn't happen to be him or know him would you??

[@alkalait]

here's a spoiler. i can see this is going to eigendecompositions :)

[@jaihindyadav3889]

worst 🤨

[@lawfordcodner3507]

Can you make some 3 variables linear equations word problems in investment, finance and mixtures thank you.