Hermann Grassmann

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Grassmann, Hermann

 

Born Apr. 15, 1809, in Stettin; died there Sept. 26, 1877. German mathematician. Also worked in physics and philology.

Grassmann’s work The Calculus of Extension (1844) gave the first systematic construction of the study of n-dimensional Euclidean space and led to the development of vector analysis and tensor calculus. However, because of the abstract exposition and unusual terminology, the work was difficult to understand. In A Textbook of Arithmetic, Grass-mann attempted a strict exposition of the arithmetic of integers and in the process explained the role of definition by induction. In physics, he wrote on acoustics and the magnetic interaction of currents. Grassmann’s general ideas about abstract vector spaces led him to the discovery of an important idea—the possibility of studying color sensations as three-dimensional vectors, which is the basis for the modern study of color. He established the laws (1853) of color mixing. Grassmann also compiled a comprehensive dictionary of the hymns of Rig Veda (a monument of ancient Indian literature).

WORKS

Gesammelte mathematische und physikalische Werke, vols. 1–3. Leipzig, 1894–1911.

REFERENCE

Klein. F. Lektsii o razvitii matematiki ν 19 stoletii, part I. Moscow-Leningrad, 1937. (Translated from German.) [7–755-l]
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The concentration dependent prolongation of the lag time or of the late protein oxidation of these terpenoids was already shown by Grassmann and coworkers (2001).
One of the many benefits of this finer stratification is that it is closed under Grassmann duality, taking [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Grassmann bemerkt, da[beta] ksadman- hier eigentlich im Dual stehen sollte.
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There are no Grassmann variables, q-numbers or field operators and their associated commutation relations.
The multiplicity of mechanisms can be categorized as acting up- or down-stream of the actual drug target or at the target site itself (Efferth and Grassmann 2000; Efferth and Volm, 2005).
In [5] the purity was proved for a certain weakly separated set-system inside the so-called positroid defined by a Grassmann necklace N.
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For jaghri- 'dripping, splashing' (ghr 'drip', see Grassmann, WB: 464; Geldner, RV I: 223f.
Geometric analogues of HRR [5] can be constructed if one defines binding by the geometric product, a notion introduced in 19th century works of Grassmann [11] and Clifford [8].
The Grassmann algebra [lambda] = [direct sum][[lambda].