4. Euclidean methods

This section introduces geometric methods for solving linear equations, both from an exact and approximate point of view (through the concept of pseudo-solutions). The methods of Jacobi, bisection and iterated QR are intended for the calculation of eigenvalues and are covered in another article.

We'll consider a real or complex Euclidean vector space E of dimension n, i.e., a vector space provided with a scalar product and the norm derived from it. We'll note (x½y) the scalar product of two vectors x and y and $\Vert x\Vert$ the norm of a vector x (it's actually N ₂ (x )). If an orthonormal basis (e ₁ ,..., e _...