Invertible change of basis matrix | Linear Algebra | Khan Academy

Using an invertible change of basis matrix to go between different coordinate systems

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[fashionvella]

Thank you soo much Sal. You have build the Linear Algebra from basic to advance in a very beautiful way. Hats off to you.

[villagehomeboy]

question: Isn't C always going to be invertible since it is a basis? And by definition, isn't a basis a set of linearly independent vectors? So by this reasoning, we can solve for [a]b by solving for the system of equations (your previous video) but also taking the inverse of C (the current video)?

by the way, these videos are very helpful. Thank you.

[zawette]

can anyone help me please
our teacher wrote this :
d'=p^-1 dp
p is the change of basis matrix
d' is the matrix with coordinate in respect of the change of basis matrix