Change of coordinates

Computing the change of coordinates matrix from a basis B to a basis C and using this to calculate new coordinates given old coordinates.
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[@drpeyam]

Note: At the end, it should be: -3 1 -5 2 And the answer is -5 -8

[@chahine__8296]

I was getting crazy lmao, i had found -5 -8 from the start but I hadnt checked the comments, so i was doing it again and again to find my mistake. Phewww

[@jiyoonpark5022]

Every time I search youtube for a linear algebra video: “I hope Dr Peyam covered this topic..”

[@maxpercer7119]

I like how you went through the 'slow way' first, which sets up the motivation for the transition matrix (and also helps define it), instead of just presenting the transition matrix unmotivated.

[@Behroozifyable]

Yes I would say the same. The rref gives - 3. 1 -5. 2 And the x goes to - 5, - 8 but otherwise a fantastic video!

[@newtonnewtonnewton1587]

Wonderful doctor peyam

[@Rundas69420]

The grade I got for my linear algebra 1 exam was not enough, so I hope that you will cover as much as possible that I can take this exam once more with a better understanding of the topics. You are just better at explaining than my professor or their scientific assistants. :D

[@drpeyam]

Thank you!!! All the videos are up already, just look at my playlists

[@Rundas69420]

@@drpeyam I know that. Thanks man :)

[@allstar965]

Very informative!

[@Debg91]

I have just got a new mobile device and I am testing its resolution with your video. Math never looked so neat!

[@drpeyam]

Glad you like the resolution 🙂

[@yaaryany]

Awesome🙌

[@sugarfrosted2005]

This is cute, you're essential doing a change of basis to the standard basis to get the transformation matrix.

[@drpeyam]

Yep ☺️

[@maxpercer7119]

I just had one question, you defined the change of basis matrix P_ {C

[@drpeyam]

P_B is in another video, it’s just P E

[@maxpercer7119]

​@@drpeyam ​ That makes sense. I drew up in Latex your argument for the change of basis matrix formula waa.ai/fLyZ.png (i keep wanting to make touch ups for the latex document, but its quite nice how elegant and tidy linear algebra is)

[@wolframalpha8634]

Hey Dr.Payam!! 😊

[@drpeyam]

Hello! 😁

[@wolframalpha8634]

@@drpeyam can I ask you a question?☺

[@aneeshsrinivas892]

Dr peyam ive been wondering something about coordinate vectors with respect to a basis denoted the way it is.Why is the coordinates of [X] with respect to B denoted X_B shouldnt it be X^B so that the identity [Id]_B^C[X]^B makes more sense as the superscript and subscripts cancel just like how [T]_Y^Z*[U]_X^Y=[TU]_X^Z. They messed up on the notation here.

[@drpeyam]

Pedagogically it’s nicer to write X_B, otherwise people think it’s exponention

[@aneeshsrinivas892]

B is an ordered pair of ordered pairs and i dont think raising vectors to vectors makes much sense here though

[@ssdd9911]

12:34 shouldn't the top right be |-3 1]?

[@ssdd9911]

that means the answer is [-5] [-8]

[@drpeyam]

Indeed!