Matrix Algebra For Physicists

A complete college-level course for engineers, computer scientists or physicists

This book provides an in depth discussion of Loewner’s theorem on the characterization of matrix monotone functions. The author refers to the book as a ‘love poem,’ one that highlights a unique mix of algebra and analysis and touches on numerous methods and results. The book details many different topics from analysis, operator theory and algebra, such as divided differences, convexity, positive definiteness, integral representations of function classes, Pick interpolation, rational approximation, orthogonal polynomials, continued fractions, and more. Most applications of Loewner’s theorem involve the easy half of the theorem.

aster the deeper layers of algebraic theory with a focus on rings, fields, and polynomial symmetries.

Quantum Decoherence, Entropy, and Gravity from Entropic Principles: From Density Matrices to Modified Einstein Equations