An illustration of a magnifying glass. An illustration of a magnifying glass.

The Hermitian Lanczos method for Hermitian matrices has a well-known connection with a 3-term recurrence for polynomials orthogonal on a discrete subset of ℝ. This connection disappears for normal ...

Abstract: An approach is presented to 2-D system stabilization by constant state feedback that is based on assigning a closed-loop matrix that is two-dimensionally (2-D) similar to a stable normal ...

Ky Fan maximum principle is a well-known observation about traces of certain hermitian matrices. In this note, we derive a powerful extension of this claim. The extension is achieved in three ways.

Abstract: It is known from the transformation theory of matrices that normal matrices can be brought to thed iagonal form by means of a similarity transformation. On the other hand, any diagonal ...

Simple normal forms are given for symmetric, skew symmetric, and general complex matrices. These three cases can be combined into a single one, if one considers matrices with elements in a suitable ...

We study the solvability of the equation AX + XA * = XA + A * X = I. In particular, we obtain various criteria for the normality of A in terms of Hermitian solutions of the equation which satisfy ...

[1] Kh. Ikramov, “On the Matrix Equation ,” Moscow University Computational Mathematics and Cybernetics. Vol. 34, No. 2, 2010, pp. 51-55. doi:10.3103 ...