If I am asked to find the number of ordered bases of a finite-dimensional vector space over $\mathbb F_p$, what does that mean? Thanks!
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It means the number of linearly independent $n$-tuples of vectors, if the space has dimension $n$. It is the same as the number of $n\times n$ invertible matrices over $\mathbb F_p$ because any two bases are related by one of those. |
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It just means that $\{a,b,c\}$ is counted separately from $\{a,c,b\}, \{c,a,b\}$ etc. |
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