April 2022 - MATHESIS

April 28, 20220Comments

Linear transformations of the plane: determinant, bases and inversion

The linear transformations of the Euclidean plane are the invertible linear applications, i.e. of non-zero determinant. They allow us to move from one basis of the plane to another, and

Algebra

Geometry

April 23, 20220Comments

The bases of the Euclidean plane: vectors and coordinates

The representation of the Euclidean plane as the Cartesian product \(\mathbb R^2\) allows us to decompose any vector of the plane into two coordinates, its abscissa and its ordinate. This

Geometry

April 20, 20220Comments

Vector rotations of the plane: the analytical approach

The vector rotations of the plane (i.e. centred in the origin), are derived analytically (by coordinates) as linear applications of determinant \(1\), which makes it possible to characterise them integrally