Nicoco Posted January 21, 2005 Share Posted January 21, 2005 Suppose you have a base {e_1, e_2, e_3} in R_3. You don't know anything else about them. Is it possible, if you are given another base {u_1, .. , u_3} to give a change-of-base matrix from the e_i's to the u_i's??? Thanks! Link to comment Share on other sites More sharing options...
matt grime Posted January 21, 2005 Share Posted January 21, 2005 yes. write u_i in terms of the e_i, presumably one is given in terms of the other, even in a general form. Link to comment Share on other sites More sharing options...
Dave Posted January 21, 2005 Share Posted January 21, 2005 That's how I did it in the Linear Algebra course. Basically: u_1 = a_{11} e_1 + a_{21} e_2 + a_{31} e_3 u_2 = a_{12} e_1 + a_{22} e_2 + a_{32} e_3 u_3 = a_{13} e_1 + a_{23} e_2 + a_{33} e_3 and then your change of basis matrix is (a_{ij}). I think. It's been a while since I've done this Link to comment Share on other sites More sharing options...
matt grime Posted January 22, 2005 Share Posted January 22, 2005 Up to transpose that is correct. Though I can never remember which way round it is. The OP should do the mental maths to figure out which way round it is. Link to comment Share on other sites More sharing options...
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