Magic Toeplitz Matrix and Its Application in Laplace PDE, Markov Chain Models and Color Vision

Eugene Demidenko

DHMC / Dartmouth Mathematics Dept

I will introduce a family of matrices that emerge in connection with several applied mathematics problems, including modeling electric potential on a disk via Laplace equation, stationary Markov chains and color vision. I called this matrix "magic Toeplitz matrix" because the sum of elements in each row and column is the same. This matrix plays a central role in the generalized Ohm's law on the disk with a circular resistivity and a finite number of electrodes. Its connection to breast cancer diagnostic is outlined. Further applications are discussed. The talk is accessible to graduate and math major junior/senior undergraduate students.

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