Explore the innovative concept of Maxel theory in this 33-minute lecture from the Math Foundations series. Dive into a pixel-by-pixel approach to matrix theory that breaks free from traditional rectangular array boundaries. Learn about maxels as msets of pixels, their algebraic properties reflecting label space geometry, and their realm-forming capabilities under various operations. Discover a unique multiplicative structure rooted in pixel-level interactions, featuring an intriguing empty aspect rarely seen in modern mathematics. Gain insights into applications in linear algebra and understand how this new thinking challenges conventional matrix theory.