1. Duality. Covariance and contravariance in a vector space

Consider a vector space E of dimension n over a field K.

Most commonly, K designates the $ℝ$ body of reals, the $ℚ$ body of rationals or the $ℂ$ body of complexes.

1.1 Physicists' vectors. Contravariance

Let ${(e_{i})}_{1 \leq i \leq n}$

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