2. Finite-dimensional linear algebra

In this section, we focus on finite-dimensional vector spaces. These are defined as follows.

Definition 26. A finite-dimensional vector space is any vector space that admits a finite generating family.

This category includes vector spaces $ℝ^{n}$ and $ℂ^{n}$ whose canonical basis is, of course, a finite generating family.

In this context, we propose to study the problem of the existence of bases, supplementary subspaces and so on.

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Finite-dimensional linear algebra