# Basis change --- Introduction ---

This is a classical exercise on vector spaces: one gives a new basis $ℬ$ of ${ℝ}^{n}$ as well as a vector $u$ written under the standard basis of ${ℝ}^{n}$, and you should find the coefficients of $u$ in the basis $ℬ=\left({v}_{1},{v}_{2},\cdots ,{v}_{n}\right)$, that is the real numbers ${c}_{i}$ $\left(i=1,\dots ,n\right)$ such that :
$u={\sum }_{i=1}^{n}{c}_{i}{v}_{i}$.

Other exercises on: Basis   Vectors   Vector space   Linear algebra

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