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Mathematics
Linear and Abstract Algebra
Show that there is a basis C of V so that C* = Λ
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[QUOTE="mathmari, post: 6770987, member: 558163"] Why must $M$ exist? Could you explain it further to me? (Wondering) So $M$ is the transformation matrix of basis from $B^{\star}$ to $\Lambda$. Let $S:=(M^{-1})^T$. Let $C$ be the basis that we get by the transformation matrix $S$ from the basis $B$. From the first question we have then that $\left (S^{-1}\right )^T$ is the transformation matrix of basis from the dual basis $B^{\star}$ to the dual basis $C^{\star}$. Since $\left (S^{-1}\right )^T=M$ and $M$ is the transformation matrix from $B^{\star}$ to $\Lambda$, it follows that $\Lambda=C^{\star}$. Is everything correct? Could we improve something? (Wondering) [/QUOTE]
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Show that there is a basis C of V so that C* = Λ
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