# Transition Matrices

I am given a set of vectors $S$ and that they are a basis of a vector space $V$. I am told that there is also another basis {$v_1,v_2,v_3,v_4$} for $V$. I need to find a transition matrix $A$ from the basis {$v_1,v_2,v_3,v_4$} to $S$.

I am not understanding what a transition matrix is. Reading: http://www.math.hmc.edu/calculus/tutorials/changebasis/changebasis.pdf made me think that it was the coefficient matrix of $S$, but that can't be true. Help?

• Yes, it is the coefficient matrix of $S$, but expressed on the basis $V$. What does the question tell you that relates $S$ to $V$? – apt1002 Dec 3 '13 at 3:09
• @apt1002 That $S$ is a basis of $V$, but I tried entering the the coefficient matrix of S: imgur.com/lITcAw7 and it was wrong – user113027 Dec 3 '13 at 3:14
• a transition matrix as I read it here, is a matrix that "converts" a vector expressed in terms of vectors in V into the "equivalent" vector in terms of S (think of Change of basis theorem) That is in essence the coefficient matrix as some call it – imranfat Dec 3 '13 at 3:15
• @imranfat Then what did I do wrong? – user113027 Dec 3 '13 at 3:16
• Is there some number example that we can look into. As far now, I do not know what you did wrong – imranfat Dec 3 '13 at 3:17