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# Topic: Exponential map

###### In the News (Tue 21 May 13)

 Articles - Exponential function   (Site not responding. Last check: 2007-10-12) The importance of exponential functions in mathematics and the sciences stems mainly from properties of their derivatives. The exponential function maps any line in the complex plane to a logarithmic spiral in the complex plane with the center at the origin. The "exponential map" sending a Lie algebra to the Lie group that gave rise to it shares the above properties, which explains the terminology. www.centralairconditioners.net /articles/Exponential_function   (1196 words)

 Exponential function Article, Exponentialfunction Information   (Site not responding. Last check: 2007-10-12) This can be seen by noting that the case of a line parallel with the real or imaginaryaxis maps to a line or circle. The "exponential map" sending a Lie algebra to the Lie group that gave rise to it shares the above properties, which explains theterminology. Similarly,since the Lie algebra M(n, R) of all square real matrices belongs to the Lie group of all invertiblesquare matrices, the exponential function for square matrices is a special case of the Lie algebra exponential map. www.anoca.org /real/functions/exponential_function.html   (853 words)

 tetration.org - Home Page Tetration is defined as iterated exponentiation but while exponentiation is essential to a large body of mathematics, little is known about tetration due to its chaotic properties. Mathematicians have been researching tetration since at least the time of Euler but it is only at the end of the twentieth century that the combination of advances in dynamical systems and access to powerful computers is making real progress possible. Although his contributions to this project of three decades are different from my own, I consider them of equal importance. www.tetration.org   (388 words)

 CIS 610 Handout 1 Least squares, Pseudo-inverses, Minimization of quadratic functions using Lagrange multipliers Lie Groups and Lie Algebras, the exponential map, part I Lie Groups and Lie Algebras, the exponential map, part II www.cis.upenn.edu /~jean/lecnotes/agm2003.html   (138 words)

 CS 15-497/15-861, Spring '02, Syllabus Appendix B.4 Parent for a review of splines Practical Parameterization of Rotations Using the Exponential Map, Grassia Spherical averages and applications to spherical splines and interpolation Samuel R. Buss, Jay P. Fillmore ACM Transactions on Graphics (TOG) April 2001 Volume 20 Issue 2 www.cs.cmu.edu /~jkh/anim_class.html   (1546 words)

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