The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

Abstract The effect of matrix perturbations on the polar decomposition has been studied by several authors and various results are known. However, for operators between infinite-dimensional spaces the ...

IMAGINE discovering an ancient treasure chest sealed with a complex dual-lock mechanism, requiring two keys that must work together in a precise way. A matrix—a rectangular array of numbers—is like a ...