Explore the concept of rigid matrices derived from rectangular probabilistically checkable proofs (PCPs) in this 22-minute IEEE conference talk. Delve into the fundamentals of rigid matrices and low-rank matrices before examining various constructions. Investigate the role of PCPs in decision procedures and engage with a thought experiment. Learn about rectangular PCPs, prime and B prime concepts, and their implications. Gain insights from speakers Amey Bhangale, Prahladh Harsha, Orr Paradise, and Avishay Tal as they guide you through this complex topic, from introduction to conclusion.