# DIS

## Seminar

### The Sylvester equation, Cauchy matrices and matrix discrete integrable systems

Seminar Room 1, Newton Institute

#### Abstract

The Sylvester equation, AM+ MB = C, is a famous matrix equation in linear algebra and widely used in many areas. Solution (M) of the equation is usually given through matrix exponential functions and integrals. In the talk, we will give an explicit form of M as solutions to the Sylvester equation. Then, starting from the Sylvester equation and introducing suitable shift relations to define plane wave factors, we construct matrix discrete integrable systems of which solutions are explicitly expressed via Cauchy matrices.#### Video

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