Let $B$ and $C$ be two bases. To find the change of basis matrix $\phi_{B,C}$, I compute $\phi_{SB,B}$ and $\phi_{SB,C}$. Create the new matrix $T=[\phi_{SB,B}|\phi_{SB,C}]$. Reducing it to reduced row echelon form, should yield $T=[I|\phi_{B,C}$, right? Is there a way to verify that the new basis indeed maps $[v]_B$ to $[v]_C$?
Change of basis matrix verification
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matrices
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1What are $\phi_{SB, B}$ and $\phi_{SB, C}$? – 2012-01-19
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0@Leandro The change of basis from the standard basis to B, respectively C. – 2012-01-19