A remark on normal forms of matrices

Smith Normal Forms of Incidence Matrices

A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current understanding are indicated.

Normal forms for general polynomial matrices

We present an algorithm for the computation of a shifted Popov Normal Form of a rectangular polynomial matrix. For specific input shifts, we obtain methods for computing the matrix greatest common divisor of two matrix polynomials (in normal form) or such polynomial normal form computation as the classical Popov form and the Hermite Normal Form. The method is done by embedding the problem of co...

A Remark on a Norm Inequality for Square Matrices

On higher rank numerical hulls of normal matrices

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

Fast Computation of Hermite Normal Forms of Random Integer Matrices

This paper is about how to compute the Hermite normal form of a random integer matrix in practice. We propose significant improvements to the algorithm by Micciancio and Warinschi, and extend these techniques to the computation of the saturation of a matrix. Tables of timings confirm the efficiency of this approach. To our knowledge, our implementation is the fastest implementation for computin...