Tag
Linear Algebra & Lattices
7 resources tagged “Linear Algebra & Lattices” across the knowledge library.
7 items
Guide6 Aug 2026Applications of the LLL AlgorithmPractical applications of lattice reduction: integer kernel and image computation, integer relation detection, recovering minimal polynomials from numerical approximations, and simultaneous Diophantine approximation.5 min readRead MoreGuide6 Aug 2026Gram–Schmidt OrthogonalisationThe Gram-Schmidt procedure, the mu coefficients and their role in reduction conditions, the numerical instability of the classical algorithm, and exact integral alternatives.4 min readRead MoreGuide6 Aug 2026Lattices and Quadratic FormsLattices as discrete subgroups, bases and unimodular change of basis, the Gram matrix and determinant, successive minima, and the correspondence with positive definite quadratic forms.4 min readRead MoreGuide6 Aug 2026Linear Algebra Algorithms over Fields and RingsExact Gaussian elimination, fraction-free elimination, determinant and characteristic polynomial algorithms, and kernel and image computation over fields and over ℤ.5 min readRead MoreGuide6 Aug 2026The Hermite Normal FormDefinition and uniqueness of the Hermite normal form, algorithms for computing it, entry explosion and its remedies, and its role as the representation of choice for modules and ideals.5 min readRead MoreGuide6 Aug 2026The LLL Lattice Reduction AlgorithmThe LLL algorithm: reduction conditions, the swap-and-reduce loop, the potential function that proves polynomial termination, quality guarantees, and the deep-insertion and floating-point variants.5 min readRead MoreGuide6 Aug 2026The Smith Normal Form and Its ApplicationsThe Smith normal form, elementary divisors, the structure theorem for finitely generated abelian groups, and the application to class group structure determination.4 min readRead More