2. Changing bases
Given a linear application f from one vector space into another, one objective is to find bases relative to which the matrix of f has a simple form: diagonal, block diagonal...
For this purpose, we often need to change bases in a vector space.
This is what we focus on in this section, in particular by explaining the formulas for changing bases for the components of a vector and the matrices of a linear application.
2.1 Passage matrices
Definition 8. Consider a vector space E, of dimension n, and two bases thereof:
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Changing bases
Matrix rank
