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German polymath, linguist and mathematician (1809–1877)
Hermann Günther Grassmann (German: Graßmann, pronounced [ˈhɛʁman ˈɡʏntɐ ˈɡʁasman]; 15 April 1809 – 26 September 1877) was a German polymath known in his
Hermann_Grassmann
Algebra associated to any vector space
v} in V . {\displaystyle V.} The exterior algebra is named after Hermann Grassmann, and the names of the product come from the "wedge" symbol ∧ {\displaystyle
Exterior_algebra
Surname list
Graßmann (1920–1991), German Luftwaffe pilot Hans Grassmann (born 1960), German physicist Hermann Grassmann (1809–1877), German linguist, physicist, and mathematician
Grassmann_(surname)
Anticommutating number
In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the
Grassmann_number
Perception of color mixtures
related to one another in a color matching context. Discovered by Hermann Grassmann these "laws" are actually principles used to predict color match responses
Grassmann's laws (color science)
Grassmann's_laws_(color_science)
Dissimilatory sound law
IPA § Brackets and transcription delimiters. Grassmann's law, named after its discoverer Hermann Grassmann, is a dissimilatory phonological process in
Grassmann's_law
Integration for Grassmann variables
Berezin (also known as Grassmann integral, after Hermann Grassmann) is a way to define integration for functions of Grassmann variables (elements of the
Berezin_integral
Mathematical space
Grassmannian is named for the German polymath, linguist and mathematician Hermann Grassmann, who introduced the concept to mathematics. The earliest work on a
Grassmannian
Embedding of a Grassmannian into projective space
space). The image of that embedding is the Klein quadric in RP5. Hermann Grassmann generalized Plücker's embedding to arbitrary k and n. The homogeneous
Plücker_embedding
polymath Hermann Grassmann: Grassmann's laws Grassmann algebra Grassmann bundle Grassmann dimensions Grassmann graph Grassmann integral Grassmann number
List of things named after Hermann Grassmann
List_of_things_named_after_Hermann_Grassmann
coordinate-free way. The technique is based on work by German mathematician Hermann Grassmann on exterior algebra, and subsequently by British mathematician Arthur
Grassmann–Cayley_algebra
Standard that defines a specific range of colors
points in color space. The color-space concept was likely due to Hermann Grassmann, who developed it in two stages. First, he developed the idea of vector
Color_space
Branch of mathematics
concepts and applications involve single vectors, mathematicians such as Hermann Grassmann considered structures involving pairs, triplets, and multivectors
Multilinear_algebra
German mathematician (1839–1873)
that Hermann Grassmann had developed in his Extension Theory in two publications. This was the first of many references later made to Grassmann's early
Hermann_Hankel
First sacred canonical text of Hinduism
khila hymns have sanctified roles in rituals from ancient times). Hermann Grassmann had numbered the hymns 1 through to 1028, putting the vālakhilya at
Rigveda
Axioms for the natural numbers
formalizing arithmetic was not well appreciated until the work of Hermann Grassmann, who showed in the 1860s that many facts in arithmetic could be derived
Peano_axioms
(essayist) Thorold Gosset (lawyer) Jørgen Pedersen Gram (actuary) Hermann Grassmann (school teacher) John Graunt (haberdasher) George Green (miller) Aubrey
List of amateur mathematicians
List_of_amateur_mathematicians
German mathematician (1843 to 1905)
mathematician. He is remembered for promoting the geometric algebra of Hermann Grassmann and for a method of visualizing polytopes called Schlegel diagrams
Victor_Schlegel
Algebraic operation on coordinate vectors
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Dot_product
Branch of mathematics
nor is there anything to suggest they suffered thereby." In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new
Linear_algebra
Set of vectors used to define coordinates
père et fils Grassmann, Hermann (1844), Die Lineale Ausdehnungslehre - Ein neuer Zweig der Mathematik (in German), reprint: Hermann Grassmann. Translated
Basis_(linear_algebra)
German mathematician (1861–1941)
after Engel's death. He was also the editor of the collected works of Hermann Grassmann. Engel translated the works of Nikolai Lobachevski from Russian into
Friedrich Engel (mathematician)
Friedrich_Engel_(mathematician)
Algebraic object with geometric applications
tensors, and the Riemann curvature tensor. The exterior algebra of Hermann Grassmann, from the middle of the nineteenth century, is itself a tensor theory
Tensor
Class of simple graphs defined from vector spaces
In graph theory, Grassmann graphs are a special class of simple graphs defined from systems of subspaces. The vertices of the Grassmann graph Jq(n, k) are
Grassmann_graph
Algebraic structure designed for geometry
dimensions. The geometric product was first briefly mentioned by Hermann Grassmann, who was chiefly interested in developing the closely related exterior
Geometric_algebra
British mathematician and philosopher (1845–1879)
a British mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra. This is a special
William_Kingdon_Clifford
Name list
(1893–1946), leading member of the NSDAP Hermann Grassmann (1809–1877), German linguist and mathematician Hermann Gundert, a German missionary who compiled
Hermann_(name)
Colour space defined by the CIE in 1931
700 nm (red) light (accounting for luminosity). In 1853, Hermann Grassmann developed Grassmann's laws, which aimed to describe color mixing algebraically
CIE_1931_color_space
Use of coordinates for representing vectors
with vectors in the same publication. Vector ideas were advanced by Hermann Grassmann in 1841, and again in 1862 in the German language. But German mathematicians
Vector_notation
Principal square root of minus 1
a bivector. Hestenes, David (1996). "Grassmann's Vision" (PDF). In Schubring, G. (ed.). Hermann Günther Graßmann (1809–1877). Boston Studies in the Philosophy
Imaginary_unit
Mathematical function, in linear algebra
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Linear_map
Differential form of degree one or section of a cotangent bundle
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
One-form
British physicist
who built on the fundamental work of William Kingdon Clifford and Hermann Grassmann. In 1998, together with Lasenby and Gull, he proposed the gauge theory
Chris_J._L._Doran
Day of the year
Ferdinand Möbius, German mathematician and astronomer (born 1790) 1877 – Hermann Grassmann, German mathematician and physicist (born 1809) 1902 – Levi Strauss
September_26
Matrix operation which flips a matrix over its diagonal
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Transpose
Mathematical operation on vector spaces
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Tensor_product
Element of an exterior algebra
have properties similar to the homogeneous coordinates of points, called Grassmann coordinates. Points in a real projective space Pn are defined to be lines
Multivector
19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, William Rowan Hamilton
19th_century_in_science
Array of numbers describing a metric connection
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Christoffel_symbols
Mathematical concept
Univalent foundations are inspired both by the old Platonic ideas of Hermann Grassmann and Georg Cantor and by "categorical" mathematics in the style of
Univalent_foundations
Exterior algebraic map taking tensors from p forms to n-p forms
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Hodge_star_operator
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Kronecker_delta
Property of a mathematical space
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Dimension
Method for specifying point positions
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Coordinate_system
Study of the history and culture of South Asia
(1791–1867) Duncan Forbes (linguist) (1798–1868) James Prinsep (1799–1840) Hermann Grassmann (1809–1877) John Muir (indologist) (1810–1882) Edward Balfour (1813–1889)
Indology
American philosopher
attended the Stettin Gymnasium where he studied mathematics under Hermann Grassmann. He later studied at the universities of Strassburg (then Germany
Paul_Carus
Physical law
including Wilhelm Weber, Rudolf Clausius, Maxwell, Bernhard Riemann, Hermann Grassmann, and Walther Ritz, developed this expression to find a fundamental
Ampère's_force_law
Operation that pairs a left and a right R-module into an abelian group
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Tensor_product_of_modules
Shorthand notation for tensor operations
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Einstein_notation
Number used for counting
the logical rigor in the foundations of mathematics. In the 1860s, Hermann Grassmann suggested a recursive definition for natural numbers, thus stating
Natural_number
Covariant derivative of the metric tensor
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Nonmetricity_tensor
Coordinate-free definition of a tensor
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Tensor_(intrinsic_definition)
Austrian mathematician
— outside his teaching activity — on mathematical problems like Hermann Grassmann's "Ausdehnungslehre" (theory of extension, or exterior algebra). Frank
Hermann_Rothe
Mathematical operation on vectors in 3D space
physics education. In 1844, Hermann Grassmann published a geometric algebra not tied to dimension two or three. Grassmann developed several products,
Cross_product
Common elements of two or more sets
Mathematical Operators. The symbol U+2229 ∩ INTERSECTION was first used by Hermann Grassmann in Die Ausdehnungslehre von 1844 as general operation symbol, not
Intersection
astronomer, engineer, mathematician and physicist. Dropped out of college. Hermann Grassmann, polymath Michael Faraday, a chemist and physicist. Although Faraday
List_of_autodidacts
Graphical notation for multilinear algebra calculations
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Penrose_graphical_notation
Mathematical notation
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Multi-index_notation
Topological space that locally resembles Euclidean space
every submanifold of Euclidean space is locally the graph of a function. Hermann Weyl gave an intrinsic definition for differentiable manifolds in his lecture
Manifold
Tensor invariant under permutations of vectors it acts on
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Symmetric_tensor
Object in geometric algebra
in showing that the quaternion algebra is just a special case of Hermann Grassmann's "theory of extension" (Ausdehnungslehre). Hestenes defined a rotor
Rotor_(mathematics)
proposed by Hermann Grassmann in 1863, though the name "aspirate throwback" appears later. The second clause is now referred to alone as Grassmann's law. Bartholomae's
Glossary of sound laws in the Indo-European languages
Glossary_of_sound_laws_in_the_Indo-European_languages
Scientific technique used in historical linguistics
that they had discovered. Although Hermann Grassmann explained one of the anomalies with the publication of Grassmann's law in 1862, Karl Verner made a methodological
Comparative_method
Real numbers adjoined with a nil-squaring element
between them. The n-dimensional generalization, the Grassmann number, was introduced by Hermann Grassmann in the late 19th century. In modern algebra, the
Dual_number
System of moving vectors in differential geometry
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Parallel_transport
Specification of a derivative along a tangent vector of a manifold
It was soon noted by other mathematicians, prominent among these being Hermann Weyl, Jan Arnoldus Schouten, and Élie Cartan, that a covariant derivative
Covariant_derivative
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Moment_of_inertia
Decomposition in multilinear algebra
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Tensor_rank_decomposition
Goldbach Kurt Gödel Adolph Göpel Rudolf Gorenflo Lothar Göttsche Hermann Grassmann Heinrich Friedrich Gretschel Michael Griebel Martin Grötschel Detlef
List_of_German_mathematicians
Tensor used in general relativity
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Einstein_tensor
differential equations, and George Boole freely employed them. Hermann Grassmann and Hermann Hankel made great use of the theory, the former in studying
History_of_calculus
Tensor equal to the negative of any of its transpositions
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Antisymmetric_tensor
Array of numbers
ed. (1978), Abrégé d'histoire des mathématiques 1700-1900, Paris, FR: Hermann Hawkins, Thomas (1972), "Hypercomplex numbers, Lie groups, and the creation
Matrix_(mathematics)
Geometric object that has length and direction
century, including Augustin Cauchy, Hermann Grassmann, August Möbius, Comte de Saint-Venant, and Matthew O'Brien. Grassmann's 1840 work Theorie der Ebbe und
Euclidean_vector
Tensor operator generalizes the notion of operators which are scalars and vectors
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Tensor_operator
Textbook by E. B. Wilson based on the lectures of J. W. Gibbs
description of elliptic harmonic motion and the case of stationary waves. Hermann Grassmann had introduced basic ideas of a linear space in 1844 and 1862, and
Vector_Analysis
Tensor in differential geometry
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Ricci_curvature
Topics referred to by the same term
related to algebraic topology A1, an 1844 paper by mathematician Hermann Grassmann A1, the alternating group on a set with one only element A.1 scale
A1
Continuous surjection satisfying a local triviality condition
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Fiber_bundle
Type of vector space in math
163 Deitmar 2005, p. 26. Dieudonné 1960 Largely from the work of Hermann Grassmann, at the urging of August Ferdinand Möbius (Boyer & Merzbach 1991,
Hilbert_space
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Symmetrization
Isomorphism between the tangent and cotangent bundles of a manifold
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Musical_isomorphism
Leibnizian universal language concept
Gödel. Wellesley MA: A. K. Peters. Fearnley-Sander, Desmond, 1982. "Hermann Grassmann and the Prehistory of Universal Algebra," The American Mathematical
Characteristica_universalis
Construct in differenital geometry
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Metric_connection
Mathematical notation for tensors and spinors
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Abstract_index_notation
Straight path on a curved surface or a Riemannian manifold
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Geodesic
of things named after Évariste Galois List of things named after Hermann Grassmann List of things named after Alexander Grothendieck List of things named
Lists_of_mathematics_topics
Expression that may be integrated over a region
aspects of the exterior algebra of differential forms appears in Hermann Grassmann's 1844 work, Die Lineale Ausdehnungslehre, ein neuer Zweig der Mathematik
Differential_form
Construct allowing differentiation of tangent vector fields of manifolds
1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity)
Affine_connection
Notation used for Weyl spinors
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Van_der_Waerden_notation
Conserved physical quantity; rotational analogue of linear momentum
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Angular_momentum
Mapping from p forms to p-1 forms
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Interior_product
19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, William Rowan Hamilton
History_of_mathematics
Vector behavior under coordinate changes
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
German mathematician (1841–1902)
Morgan. Instead, his sources were texts by Ohm, Hankel, Hermann Grassmann, and Robert Grassmann (Peckhaus 1997: 233–296). In 1873, Schröder learned of
Ernst Schröder (mathematician)
Ernst_Schröder_(mathematician)
Tensor having both covariant and contravariant indices
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Mixed_tensor
Function that is invariant under all permutations of its variables
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Symmetric_function
Tensor describing energy momentum density in spacetime
Newtonian gravity. The electromagnetic stress–energy tensor was introduced by Hermann Minkowski in 1907, and later generalized by Max von Laue in 1911. The stress–energy
Stress–energy_tensor
Tensor index notation for tensor-based calculations
Carl Friedrich Gauss Hermann Grassmann Tullio Levi-Civita Gregorio Ricci-Curbastro Bernhard Riemann Jan Arnoldus Schouten Woldemar Voigt Hermann Weyl
Ricci_calculus
Geometric model of the physical space
came in the abstract formalism of vector spaces, with the work of Hermann Grassmann and Giuseppe Peano, the latter of whom first gave the modern definition
Three-dimensional_space
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HERMANN GRASSMANN
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HERMANN GRASSMANN
HERMANN GRASSMANN
HERMANN GRASSMANN
HERMANN GRASSMANN
HERMANN GRASSMANN
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