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Hermann Hankel (14 February 1839 – 29 August 1873) was a German mathematician. Having worked on mathematical analysis during his career, he is best known for introducing the Hankel transform and the Hankel matrix .
One of the first mathematicians to appreciate Grassmann's ideas during his lifetime was Hermann Hankel, whose 1867 Theorie der complexen Zahlensysteme. [5] […], he developed […] some of Hermann Grassmann's algebras and W.R. Hamilton's quaternions. Hankel was the first to recognise the significance of Grassmann's long-neglected writings and ...
In control theory, Hankel singular values, named after Hermann Hankel, provide a measure of energy for each state in a system. They are the basis for balanced model reduction, in which high energy states are retained while low energy states are discarded. The reduced model retains the important features of the original model.
This is a version of the Hankel contour that consists of just a linear mirror image across the real axis. In mathematics, a Hankel contour is a path in the complex plane which extends from (+∞,δ), around the origin counter clockwise and back to (+∞,−δ), where δ is an
Hankel matrices are formed when, given a sequence of output data, a realization of an underlying state-space or hidden Markov model is desired. [3] The singular value decomposition of the Hankel matrix provides a means of computing the A , B , and C matrices which define the state-space realization. [ 4 ]
The Hankel transform appears when one writes the multidimensional Fourier transform in hyperspherical coordinates, which is the reason why the Hankel transform often appears in physical problems with cylindrical or spherical symmetry. Consider a function () of a -dimensional vector r.
More precisely, the Hartle-Hawking state is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes the wave function of the universe.. It is a functional of the metric tensor defined at a (D − 1)-dimensional compact surface, the universe, where D is the spacetime dimension.
The authors argue that the current crisis in cosmology is a result of physicists making the wrong commitments to universalizing local experiments and to a block universe. They suggest instead that new research projects would be revealed if we took seriously the idea of one, and only one, universe as well as the reality of our experience of time.