MA 35100 Lecture Notes - Lecture 27: Canonical Transformation
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If i is are with basis b = ex, xn3 the point transformation for 5 with respect to b is. The coordinate transformation for 5 with respect to b is: Tb: f ->ru c. x, + cnxn"s(cr) we have tb = (te) " These let us decode and encode elements of was their b-cords. I see weanesday notes e: (reframed in p3,b= 31+x,2x,x+x2, x3 } Tb(2 + 4x + 3x" -x 3)= [2e, 3,-17. From now on, linear transfruths are called l. Let c: f - to be a linear transforth where dim t:n-say. Xn3 basis for 8 and dim to: m-say. The point in 20 with b-coord vector given by multiplying m by the. We can represent the transformation (with a unique men matrix. M, called the matrix that represents (with respect to b and b. (ineorem 3. 14) Must know what the does to the standard basis in teh: e1, .
