Change of basis vector

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Change of basis vectors can be defined as a matrix transformation. so to find the coordinates of a vectors in a different basis vectors system we can use matrix multiplication. Think of transforming our grid to the other system and finding the position of the vector in the new system. To get the co-ordinates of our vector from some one else’s grid, we can just multiply our vector with the inverse of their transformation matrix.

Converting a transformation from one system to another

• We can’t just convert the our basis vectors positions to the other system, because it would denote where our basis vectors land on the other system.
• $A^{-1}$ M A is the formula for that, where A is transformation to convert from their system to ours, and M, the transformation, and $A^{-1}$ is the. inverse transformation to convert from our system to theirs, ref:: Formula explanation