Determinants of Hessenberg L-Matrices
A determinantal formula for Hessenberg matrices is presented. The formula uses paths in an associated directed graph. The qualitative properties of Hessenberg matrices are investigated. Necessary and sufficient conditions are given for when the matrix is an L-matrix, and for when the determinant is sign positive or sign negative.
SIAM Journal on Matrix Analysis and Applications
Stuart, J. L.
(1991). Determinants of Hessenberg L-Matrices. SIAM Journal on Matrix Analysis and Applications, 12(1), 7-15.
Available at: http://aquila.usm.edu/fac_pubs/6934