Normal operators

A normal operator is a special kind of mathematical function that, when applied to a space, behaves very predictably. Specifically, it commutes with its own "adjoint" (a related, mirror-like transformation). This property ensures that the operator can be broken down into simpler parts called eigenvectors and eigenvalues, making it easier to analyze. Normal operators include important cases like symmetric or unitary operators, which appear frequently in physics and engineering. Their well-behaved nature allows for a comprehensive understanding of complex systems by simplifying their structure without losing essential information.