Nicholas J. Rose

The Index and the Drazin Inverse of Block Triangular Matrices

Bounds for the index of block triangular matrices are given in terms of the indices of the diagonal blocks. For a matrix of the form \[ M = \left[ {\begin{array}{*{20}c} A &\vline & B \\ \hline 0 &\vline & C \\ \end{array} } \right] \] where A and C are square, an explicit formula for the Drazin inverse,

Singular Perturbation of Autonomous Linear Systems

M^D

A second order singular linear system arising in electric power systems analysis

, of M is given which is a function of

The Laurent Expansion of a Generalized Resolvent with Some Applications

A,B,C,A^D

On optimal terminal control

and

An algebraic-analytic approach to nonnegative bases

C^D

Nonnegative matrices with power invariant zero patterns

only.

A Note On Computing the Drazin Inverse

Let

Results of an informal survey on the use of linear algebra in industry and government

X_\varepsilon (t) = \exp (({{A + B} /\varepsilon })t)

Applications of the Drazin Inverse to Linear Systems of Differential Equations with Singular Constant Coefficients

where A, B are