MAT211_Lecture13[1]

MAT211_Lecture13[1] - Overview A and B basis of linear...

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1 1 MAT211 Lecture 13 The matrix of a linear transformation The B-matrix of a linear transformation The columns of the B-matrix of a linear transformation Change of basis matrix Change of basis in a subspace of R n Change of basis for the matrix of a linear transformation A and B basis of linear space V, T a linear transformation from V to V. Coordinate Transformation from V to R n L(f)= [f] B B -matrix of T is L B o T o L B -1 Change of basis from B to A, S B->A =L A o (L B ) -1 If B is B -matrix of T and A is A -matrix of T, S the change of basis from B to A, AS=S B Overview 3 EXAMPLE Consider the space U of upper triangular 2 x 2 matrices and the linear transformation T from U to U deFned by T(M)=AM where A is 1 -2 0 3 ±or each element z of U, Fnd [T(z)] B, where B is the standard basis 4 DeFnition Consider a linear transformation T from V to V where V is an n-dimensional linear space. Let B denote a basis of V. The matrix B of the transformation from R
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MAT211_Lecture13[1] - Overview A and B basis of linear...

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