# Viktor Sas: A study of Kronecker product and Lyapunov equations

**Time: **
Fri 2019-03-22 09.00 - 10.00

**Location: ** Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University ￼

**Respondent: **
Viktor Sas

**Supervisor: **
Yishao Zhou

Abstract: *In this thesis we study the Kronecker product and its applications in solving matrix equations. First we will give some preliminaries as a good tool to understand the calculations we will do with the Kronecker product. The preliminaries contain material from linear algebra and ordinary differential equations (ODE). We deal with the Kronecker product togehter with the vec – operator on matrix equations. The method is then applied to a special class of matrix equations, Lyapunov equations, in particular **thier relations to stability theory for linear dynamical systems are investigated. We will also study three different methods to solve the least square problem in the formulation of Kronecker product.*