Title: Anisotropic Polarization Tensors and Detection of an Anisotropic Inclusion

Abstract: 
 We introduce the notion of (generalized) anisotropic polarization tensors and prove that they are symmetric and positive-definite. We also estimate the eigenvalues of the anisotropic polarization tensor in terms of the volume of the given domain. We apply these
properties to an electrical impedance tomography problem to detect a single anisotropic inhomogeneity of small size.  The goal is to detect an inclusion when anisotropic conductivities of the background and the inclusion are known.