Duvenhage, Rocco de VilliersVan Staden, WerndWuzyk, Jan2018-04-172018-02Duvenhage, R., Van Staden, W. & Wuzyk, J. 2018, 'Analyticity and spectral properties of noncommutative Ricci flow in a matrix geometry', Linear Algebra and its Applications, vol. 539, pp. 160-174.0024-379510.1016/j.laa.2017.11.004http://hdl.handle.net/2263/64589We study a first variation formula for the eigenvalues of the Laplacian evolving under the Ricci flow in a simple example of a noncommutative matrix geometry, namely a finite dimensional representation of a noncommutative torus. In order to do so, we first show that the Ricci flow in this matrix geometry is analytic.en© 2018 Elsevier Inc. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Linear Algebra and its Applications, vol. 539, pp. 160-174. 2018. doi : 10.1016/j.laa.2017.11.004.Ricci flowNoncommutative geometryMatrix geometrySpectrum of the LaplacianPostprint Article