![]() Represents the spherical coordinate ( theta, phi, r). If called with a single matrix argument then each row of S The inputs theta, phi, and r must be the same shape, or Transform spherical coordinates to Cartesian coordinates. = sph2cart ( theta, phi, r) = sph2cart ( S) C = sph2cart (…) Where each row represents one spherical coordinate If only a single return argument is requested then return a matrix S R is the distance to the origin (0, 0, 0). Phi is the angle relative to the xy-plane. If called with a single matrix argument then each row of C represents The inputs x, y, and z must be the same shape, or scalar. Transform Cartesian coordinates to spherical coordinates. = cart2sph ( x, y, z) = cart2sph ( C) S = cart2sph (…) Where each row represents one Cartesian coordinate If only a single return argument is requested then return a matrix C ![]() R is the distance to the z-axis (0, 0, z). Represents the polar/(cylindrical) coordinate ( theta, r If called with a single matrix argument then each row of P The inputs theta, r, (and z) must be the same shape, or Transform polar or cylindrical coordinates to Cartesian coordinates. = pol2cart ( theta, r) = pol2cart ( theta, r, z) = pol2cart ( P) = pol2cart ( P) C = pol2cart (…) Where each row represents one polar/(cylindrical) coordinate If only a single return argument is requested then return a matrix P R is the distance to the z-axis (0, 0, z). Theta describes the angle relative to the positive x-axis. Represents the Cartesian coordinate ( x, y (, z)). If called with a single matrix argument then each row of C The inputs x, y (, and z) must be the same shape, or Transform Cartesian coordinates to polar or cylindrical coordinates. 1461–1466.Next: Mathematical Constants, Previous: Rational Approximations, Up: Arithmetic ġ7.8 Coordinate Transformations = cart2pol ( x, y) = cart2pol ( x, y, z) = cart2pol ( C) = cart2pol ( C) P = cart2pol (…) 50th IEEE Conference on Decision and Control, 2011, pp. J. Rohn, “Forty necessary and sufficient conditions for regularity of interval matrices: a survey,” Electronic Journal Of Linear Algebra, vol. 18, pp. 28th IEEE Conference on Decision and Control, 1989, pp. M. Mansour, “Robust stability of interval matrices,” in Proc. J. Feigenbaum, “Directed graphs have unique Cartesian factorizations that can be found in polynomial time,” Discrete Applied Mathematics, vol. 15, pp. Vizing, “The Cartesian product of graphs,” Vycisl. G. Sabidussi, “Graph multiplication,” Mathematische Zeitschrift, vol. 72, pp. ![]() W. Imrich and S. Klavzar, Product Graphs: Structure and Recognition. Berlin: Springer, 2005.Ī. Nguyen and M. Mesbahi, “A factorization lemma for the agreement dynamics,” in 46th IEEE Conference on Decision and Control, no. 1, 2007, pp. L. Kocarev and G. Vattay, Complex Dynamics in Communication Networks. N. Ganguly, A. Deutsch, and A. Mukherjee, Dynamics on and of Complex Networks: Applications to Biology, Computer Science, and the Social Sciences. The first lemma allows perfect characterization of the larger network trajectories in terms of the factors’ unforced and forced. The chapter culminates in the presentation of two factorization lemmas. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. Hwang, “Complex networks: structure and dynamics,” Physics Reports, vol. The Cartesian product over Z-matrices is introduced as a method to decompose large Z-matrix dynamics to smaller Z-matrix factor dynamics. Plemmons, Nonnegative Matrices in the Mathematical Sciences. ![]() New York: Cambridge University Press, 1990.Ī. Berman and R. J. Princeton: Princeton University Press, 2010. M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks. Pappas, and V. Kumar, “Leader-to-formation stability,” IEEE Transactions on Robotics and Automation, vol. 20, no. 3, pp. Murray, “Consensus and cooperation in networked multi-agent systems,” Proc. ![]()
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