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My name is Claire Tomlin and this is the sixth module in a series that weamp;#39;re doing for the course eecs 221 a linear system theory at Berkeley and todayamp;#39;s module is about how a matrix representation of a linear map changes when you change the basis of the domain or the codomain or both last module we constructed the linear map itself given we constructed the matrix representation given the linear map and between the finite dimensional vector spaces and the basis and so now weamp;#39;re going to ask the question once you have the matrix representation and you change the basis how do you quickly figure out what the new matrix representation should be without having to go back to the beginning and reconstruct that matrix representation okay so weamp;#39;ll call it change of basis and what I like to do here is to keep a picture in my mind of the spaces and the corresponding the corresponding basis and then the map representation so Iamp;#39;m going to have here and Iamp;
