Understanding Idempotent Matrices and Their Invertibility 🔍

We discuss properties of idempotent matrices. These are matrices, P, for which we have P^2 = P. Natural examples of these type of operators are projections. Aside from the identity, these matrices are never invertible. We discuss how perturbations of the identity by an idempotent matrix do have nice invertibility properties.

#mikethemathematician, #mikedabkowski, #profdabkowski