Basis change --- Introduction ---

This is a classical exercise on vector spaces: one gives a new basis

ℬ

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 = (v_{1}, v_{2}, \dots, v_{n})

, that is the real numbers

c_{i}

(i = 1, \dots, n)

such that :

u = \sum_{i = 1}^{n} c_{i} v_{i}

Other exercises on:

Basis
Vectors
Vector space
Linear algebra

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