Quadratic Forms in Infinite Dimensional Vector Spaces

Focusing on the study of quadratic forms in infinite dimensional vector spaces, this work systematically presents results on denumerably infinite spaces, referred to as "~O-forms." It includes both previously published findings and new results, particularly from Ph.D. theses of students. The text serves as an introduction to the geometric algebra of these spaces, showcasing unique phenomena and employing recursive proofs that mirror finite dimensional induction. It also emphasizes the importance of understanding linear algebra without the obscurity of topological concepts in infinite dimensions.