#### Event Title

#### Description

In this talk we will study the different ways the power means of positive numbers can be extended to means of positive definite matrices. Then, we will analyze the properties these means satisfy. Among these properties, we will be interested in analytic properties such as monotonicity and convexity. Using these results, we will compare the power means with other interpolations between the Arithmetic-Geometric-Harmonic means.

#### Date of Event

March 23

#### Location

Mailman-Hollywood Auditorium 2nd Floor

Power Means of Matrices

Mailman-Hollywood Auditorium 2nd Floor

In this talk we will study the different ways the power means of positive numbers can be extended to means of positive definite matrices. Then, we will analyze the properties these means satisfy. Among these properties, we will be interested in analytic properties such as monotonicity and convexity. Using these results, we will compare the power means with other interpolations between the Arithmetic-Geometric-Harmonic means.

## Presenter Bio

Dr. Franco is an assistant professor at the University of North Florida whose research focuses on Lie theory and matrix analysis. He received his M.S. and Ph.D. in mathematics from Baylor University in Waco, TX.