Explore lattices and integral linear spans of vexels in this 34-minute mathematics video. Delve into these flexible, common, and useful algebraic objects, which serve as direct integral analogs of vector spaces. Learn about the crucial algorithm for computing a Hermite normal form basis to understand lattice structure. Discover how this technology applies to relations between different lattices and elements within a spanning set. Gain insights into key linear algebra concepts presented in a more general and powerful context, enhancing your understanding of abstract algebra and mathematical foundations.