ChangeOfBasis.md (766B)
1 # Change of Basis 2 3 Khan U3 4 5 **Definition:** Change of basis in linear algebra is the process of assuming the basis vectors to be some arbitrary linearly independent vectors. 6 7 Example: 8 9 B = { [1] [2] 10 [2] [1]} 11 12 a = 3B_1 + 2B_2 13 14 [a]\_B = [3] 15 [2] 16 17 While we have stated a to be [3 2] we are assigning it with basis' of B so in the standard coordinate system a = [8 7]. 18 19 ## Matrix Representation 20 21 The matrix representation of a change of basis is simply a matrix that we multiply all matricies under the basis by to find the true coordinates using the new basis'. 22 23 The matrix representation of a change of basis is always invertible. 24 25 ## L.T.s 26 27 Linear transformations are specified under the basis they are being applied to and do not apply under different basis'.