A framework for rank identities -- With a view towards operator algebras

Soumyashant Nayak

For every square matrix $A$ over a field $\mathbb{K}$, we have the equality $\mathrm{rank}(A)+\mathrm{rank}(I-A)=\mathrm{rank}(I)+\mathrm{rank}(A-A^2)$ where $I$ denotes the…