conference paper The generalized spectral-radius theorem: An analytic-geometric proof published yes Ludwig Elsner author 10509 10020 department International Workshop on Nonnegative Matrices, Applications and Generalizations and 8th Haifa Matrix Theory Conference Let Sigma be a bounded set of complex matrices, Sigma(m) = {A(1)...A(m) : A(i) is an element of Sigma}. The generalized spectral-radius theorem states that rho(Sigma)= <(rho)over cap>(Sigma), where rho(Sigma) and <(rho)over cap>(sigma) are defined as follows: rho(Sigma) = lim sup rho(m)(Sigma){1/m}, where rho(m)(Sigma) = sup {rho(A) : A is an element of Sigma(m)} with rho (A) the spectral radius; <(rho)over cap>(Sigma) = lim sup <(rho)over cap>(m)(Sigma){1/m}, where <(rho)over cap>(m)(Sigma) = sup {parallel to A parallel to: A is an element of Sigma(m)} with parallel to parallel to any matrix norm. We give an elementary proof, based on analytic and geometric tools, which is in some ways simpler than the first proof by Berger and Wang. ELSEVIER SCIENCE PUBL CO INC1995Haifa, Israel eng 0024-3795 A1995RC3710000810.1016/0024-3795(93)00320-Y 220151-159 Elsner, L. (1995): The generalized spectral-radius theorem: An analytic-geometric proof <em>Linear Algebra and its Applications</em>,220: 151-159. Elsner, L., 1995. The generalized spectral-radius theorem: An analytic-geometric proof. <em>Linear Algebra and its Applications</em>, 220, p 151-159. L. Elsner, “The generalized spectral-radius theorem: An analytic-geometric proof”, <em>Linear Algebra and its Applications</em>, <strong>1995</strong>, <em>220</em>, 151-159. Elsner, L. (1995). The generalized spectral-radius theorem: An analytic-geometric proof. <em>Linear Algebra and its Applications</em>, <em>220</em>, 151-159. doi:10.1016/0024-3795(93)00320-Y Elsner, L.: The generalized spectral-radius theorem: An analytic-geometric proof. Linear Algebra and its Applications. 220, 151-159 (1995). Elsner, L. (1995). The generalized spectral-radius theorem: An analytic-geometric proof. <em>Linear Algebra and its Applications</em> 220, 151-159. <div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Elsner, Ludwig. 1995. “The generalized spectral-radius theorem: An analytic-geometric proof”, Linear Algebra and its Applications, 220: 151-159.</div> L. Elsner, “The generalized spectral-radius theorem: An analytic-geometric proof”, <em>Linear Algebra and its Applications</em>, vol. 220, 1995, pp. 151-159. Elsner L. The generalized spectral-radius theorem: An analytic-geometric proof. <em>Linear Algebra and its Applications</em>. 1995;220:151-159. <div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Elsner, L. (1995). The generalized spectral-radius theorem: An analytic-geometric proof. <em>Linear Algebra and its Applications</em>, <em>220</em>, 151-159. doi:10.1016/0024-3795(93)00320-Y</div> Elsner L (1995) <br />The generalized spectral-radius theorem: An analytic-geometric proof.<br />Linear Algebra and its Applications 220: 151-159. <div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Elsner, L. (1995). The generalized spectral-radius theorem: An analytic-geometric proof (Linear Algebra and its Applications), <em>220</em>, 151-159. Gehalten auf der International Workshop on Nonnegative Matrices, Applications and Generalizations and 8th Haifa Matrix Theory Conference, ELSEVIER SCIENCE PUBL CO INC. doi:10.1016/0024-3795(93)00320-Y.</div> Elsner, Ludwig. “The generalized spectral-radius theorem: An analytic-geometric proof”. <em>Linear Algebra and its Applications</em> 220 (1995): 151-159. Elsner L (1995) <br /><em>Linear Algebra and its Applications</em> 220: 151-159. 16407722010-04-29T13:15:58Z2019-07-11T10:06:13Z