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Unformatted text preview: ◦ deﬁnes a linear transformation which we’ll call T . We now know that there is a matrix M so that T ( x ) = M x , where we use the standard basis on both sides. What is M ? EXAMPLE. Diﬀerentiation is a linear transformation from P 3 to P 2 . What is its matrix relative to the standard bases? It often happens that the linear transformation goes from a vector space V to the same vector space V . We then need just one basis B and we get the matrix for T relative to B , or just the Bmatrix for T . What happens to the matrix when we change bases? The matrices similar to a matrix A are exactly those matrix representations of the linear transformation T ( x ) = A x relative to diﬀerent bases! What does all this say about matrices that are diagonalizable? HOMEWORK: SECTION 5.4, #2, 4, 6, 8, 12, 14, 18...
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 Spring '08
 PAVLOVIC
 Linear Algebra, Vector Space, Euclidean vector, linear transformation

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