Invertible change of basis matrix | Linear Algebra | Khan Academy

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Using an invertible change of basis matrix to go between different coordinate systems
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[@fashionvella730]

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.

[@Nobody-Nowhere-Nothing]

This is ultra-mega late but I'm going to answer just in case any newcomers get confused. No, you can't invert a matrix just because it has linearly independent columns. It must also be a SQUARE matrix so that when you invert it you get the identity matrix. If it is not square then you must solve it by getting the rref of the matrix.

[@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

[@Waranle]

Thank you Sal

[@debendragurung3033]

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