# MS-20 Solving Matrix Equations

### Organizers: Qing-Wen Wang (Shanghai University) and Yang Zhang (University of Manitoba)

Matrix equations are widely used in many scientific areas such as engineering, physics, system and control theory, computer science, and information science. The research on solvability conditions and structural representations of solutions to matrix equations is of central importance in matrix algebra as well as in general mathematics. The topics in this mini-symposium focus mainly on the solvability conditions, special and general solutions, structural representations to some matrix algebraic equations over various algebraic structures including fields, division rings, regular rings and so on. Moreover, efficient computing algorithms and their applications in system, control theory, and quantum computing will be discussed and explored. This mini-symposium will provide an important opportunity for experts in linear algebra, matrix theory, ring theory and computer science to exchange ideas, to share new results, and to work in collaboration.

### Speakers

**Eric King-wah Chu**, *Projection Methods for Riccati Equations*

**Özlem Esen**, *On the Diagonal Stability of Metzler Matrices*

**David Imberti**, *Condition Number of Krylov Matrices and Subspaces via Kronecker Product Structure*

**Yan-Fei Jing**, *Recent Progress on Block Krylov Subspace Methods for Linear Systems with Multiple Right-hand Sides*

**Volha Kushel**, *Matrix Scalings and Submatrices*

**Jin Liang**, *Monotonicity of certain maps of positive definite matrices*

**Xingping Sheng**, *A relaxed gradient based algorithm for solving generalized coupled Sylvester matrix equations*

**Caiqin Song**, *On solutions to the matrix equations XB-AX=CY and XB-A\widehat{X}=CY*

**Lizhu Sun**, *Solutions of multilinear systems and characterizations for spectral radius of tensors*

**Qing-Wen Wang**, *A System of Matrix Equations over the Quaternion Algebra with Applications*

**Guihai Yu**,*The single-Hook immanants of adjacency and Laplacian marices for complete graph and cycle.*

**Yang Zhang**, *Solving Ore matrix equations*