We consider Schur function expansion for the partition function of the model of normal matrices. We show that this expansion coincides with Takasaki expansion [5] for tau functions of Toda lattice hierarchy. We show that the partition function of the model of normal matrices is, at the same time, a partition function of certain discrete models, which can be solved by the method of orthogonal po...

In this article we study Steffensen method to solve nonlinear matrix equation $X+A^T X^{(-1)}A=Q$, when $A$ is a normal matrix. We establish some conditions that generate a sequence of positive denite matrices which converges to solution of this equation.

Hermite and Smith normal form are important forms of matrices used in linear algebra. These terms have many applications in group theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Hermite and Smith normal form of large dense matrices. The main problems of the c...

Polynomially normal matrices in real indefinite inner product spaces are studied, i.e., matrices whose adjoint with respect to the indefinite inner product is a polynomial in the matrix. The set of these matrices is a subset of indefinite inner product normal matrices that contains all selfadjoint, skew-adjoint, and unitary matrices, but that is small enough such that all elements can be comple...

Polynomially normal matrices in real indefinite inner product spaces are studied, i.e., matrices whose adjoint with respect to the indefinite inner product is a polynomial in the matrix. The set of these matrices is a subset of indefinite inner product normal matrices that contains all selfadjoint, skew-adjoint, and unitary matrices, but that is small enough such that all elements can be comple...