Circulants,inversion of circulants,and some related matrix algebras

The spectral theory for circulants over $\text{R}$ or $\text{C}$ is discussed, followed by a discussion of inversion of circulants. The algebraic theory of one-generator matrix algebras and applications to circulants and some related algebras are presented. The theory of symmetric functions plays an important role. Thus the latter methods apply over arbitrary commutative rings.