David Marshall

Permanental Roots of Matrices

The purpose of this investigation is to present results concerning roots of per(A − λ I) = 0 where A is an n-square matrix over a field and I is the identity matrix. An attempt is made to relate the roots ofper(A − λ I) = 0 to the better-known characteristic values of A. Special emphasis is given to matrices over the real or complex field. Areas for further study of permanental roots are indicated, and several unsolved problems are posed.