Definition of coordinate vector/mapping/representation relative to a given basis

Created almost 9 years ago, updated about 8 hours ago

For basis $B=(b_1,\ldots,b_n)$, define $[v]_B=(c_1,\ldots,c_n)^T$ by $v=\sum_ic_ib_i$. The coordinate mapping $\phi_B:V\to\mathbb F^n$ is bijective and linear. Its inverse reconstructs a vector from its coefficient list.

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