These conditions are related to known but more restrictive properties that ensure a bidiagonal factorization as above, but with all parameters s jk , t kj nonzero. Some nonsingular matrices and their applications Nonsingular matrices with various structures involving certain sign patterns, diagonal dominance, tridiagonal, etc. , are presented. Applications include, extensions to the infinite case, Digital Circuit Dynamics, conformal mapping of doubly connected regions and double points of a Mathieu equation. We present results connecting the shape of the numerical range to intrinsic properties of a nonnegative matrix A . These results are to a large extent analogous to the Perron-Frobenius theory, especially as it pertains to irreducibility and cyclicity in the combinatorial sense.
Special attention is given to circular and elliptic numerical ranges.
Canadian Mathematical Society - Soci t math matique du Canada.