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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)
Grassmann_graph
Class of undirected graphs defined from systems of sets
Johnson graph is an open problem. Grassmann graph Holton, D. A.; Sheehan, J. (1993), "The Johnson graphs and even graphs", The Petersen graph, Australian
Johnson_graph
Mathematical space
Grassmannian G r k ( V ) {\displaystyle \mathbf {Gr} _{k}(V)} , also known as a Grassmann manifold, is a differentiable manifold that parameterizes the set of all
Grassmannian
Hermann Grassmann: Grassmann's laws Grassmann algebra Grassmann bundle Grassmann dimensions Grassmann graph Grassmann integral Grassmann number Grassmann variables
List of things named after Hermann Grassmann
List_of_things_named_after_Hermann_Grassmann
Pictorial representation of the behavior of subatomic particles
collection of Grassmann variables, and the 1/2 is to prevent double-counting (since ψiψj = −ψjψi). In matrix notation, where ψ and η are Grassmann-valued row
Feynman_diagram
Subset of a graph's vertices, including at least one endpoint of every edge
Khot, Subhash; Minzer, Dor; Safra, Muli (2018). "Pseudorandom Sets in Grassmann Graph Have Near-Perfect Expansion". 2018 IEEE 59th Annual Symposium on Foundations
Vertex_cover
Unsolved problem in computational complexity theory
Khot, Subhash; Minzer, Dor; Safra, Muli (2018), "Pseudorandom Sets in Grassmann Graph Have Near-Perfect Expansion", 2018 IEEE 59th Annual Symposium on Foundations
Unique_games_conjecture
Graph where any two nodes of equal distance are isomorphic
The Grassmann graphs. The Hamming Graphs (including Hypercube graphs). The folded cube graphs. The square rook's graphs. The Livingstone graph. After
Distance-transitive_graph
two in graphs with minimum degree 3. The Erdős–Hajnal conjecture that in a family of graphs defined by an excluded induced subgraph, every graph has either
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
Function of a matrix
matrix and χ i , χ ¯ i {\displaystyle \chi _{i},{\bar {\chi }}_{i}} are Grassmann variables, then ∫ D ( χ , χ ¯ ) exp [ 1 2 ( χ χ ¯ ) T V ( χ χ ¯ ) ] =
Hafnian
cubic surface Cayley's sextic Cayley's theorem Cayley's Ω process Chasles–Cayley–Brill formula Grassmann–Cayley algebra The crater Cayley on the Moon
List of things named after Arthur Cayley
List_of_things_named_after_Arthur_Cayley
British mathematician and philosopher (1845–1879)
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
linear algebra building upon concepts of p-vectors and multivectors with Grassmann algebra. Multiplicative number theory a subfield of analytic number theory
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
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
English mathematician (1821–1895)
theorem Cayley–Hamilton theorem in linear algebra Cayley–Bacharach theorem Grassmann–Cayley algebra Cayley–Menger determinant Cayley diagrams – used for finding
Arthur_Cayley
Superconformal Yang–Mills theory
superspace in which the spacetime variables are augmented by a number of Grassmann variables which, for the case N=4, consist of 4 Dirac spinors, making
N = 4 supersymmetric Yang–Mills theory
N_=_4_supersymmetric_Yang–Mills_theory
Upper bound on intersecting set families
(1987). Frankl & Wilson (1986); Godsil & Meagher (2015), Chapter 9: The Grassmann scheme, pp. 161–183. Frankl & Deza (1977); Cameron & Ku (2003); Larose
Erdős–Ko–Rado_theorem
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
Array of numbers
The adjacency matrix of a finite graph is a basic notion of graph theory. It records which vertices of the graph are connected by an edge. Matrices
Matrix_(mathematics)
German mathematician and astronomer (1790–1868)
and Schläfli's discovery of the 4-polytopes, Möbius (with Cayley and Grassmann) was one of only three other people who had also conceived of the possibility
August_Ferdinand_Möbius
Algebraic operation on coordinate vectors
Cauchy–Schwarz inequality Cross product Dot product representation of a graph Euclidean norm, the square-root of the self dot product Matrix multiplication
Dot_product
Four-dimensional number system
systems of the 19th century (Hamilton, Möbius, Bellavitis, Clifford, Grassmann, Tait, Peirce, Maxwell, Macfarlane, MacAuley, Gibbs, Heaviside). Doran
Quaternion
Straight path on a curved surface or a Riemannian manifold
mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold
Geodesic
English mathematician
three and higher dimensions. He also points out the applicability of Grassmann's Inner Multiplication for the expression of the distance formulae both
Homersham_Cox_(mathematician)
Generalization of the concept from statistical mechanics
effective action of a theory. When the random variables are anti-commuting Grassmann numbers, then the partition function can be expressed as a determinant
Partition function (mathematics)
Partition_function_(mathematics)
Topological space that locally resembles Euclidean space
Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the
Manifold
Type of vector space in math
Deitmar 2005, p. 26. Dieudonné 1960 Largely from the work of Hermann Grassmann, at the urging of August Ferdinand Möbius (Boyer & Merzbach 1991, pp. 584–586)
Hilbert_space
Laws in physics about force and motion
Physics: The Early Decades". In Schubring, Gert (ed.). Hermann Günther Graßmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar
Newton's_laws_of_motion
Theory of interwoven space and time by Albert Einstein
{\text{A}}} and B , {\displaystyle {\text{B}},} have been plotted on this graph so that their coordinates may be compared in the S and S' frames. Fig. 3-1b
Special_relativity
American mathematician
Pollack, Richard (1995), "Foundations of a theory of convexity on affine Grassmann manifolds", Mathematika, 42 (2): 305–328, CiteSeerX 10.1.1.48.3232, doi:10
Richard_M._Pollack
Vector space with generalized dot product
complication, in geometric algebra the inner product and the exterior (Grassmann) product are combined in the geometric product (the Clifford product in
Inner_product_space
Mathematical operation on vector spaces
a tensor product of graphs in the above sense; actually it is the category-theoretic product in the category of graphs and graph homomorphisms. However
Tensor_product
Family of polynomials
2016. (undated, 2004 or earlier). Ratnadha Kolhatkar, Zeta function of Grassmann Varieties (dated January 26, 2004) Weisstein, Eric W. "q-Binomial Coefficient"
Gaussian_binomial_coefficient
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
Geometric model of the physical space
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
City county in Podlaskie Voivodeship, Poland
from the original on 15 August 2011. Retrieved 15 March 2011. Magdalena Grassmann. "Podlaski Wersal Branickich". palac.amb (in Polish). Archived from the
Białystok
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
quaternions and deduces that they are non-commutative. 1844 - Hermann Grassmann publishes his Ausdehnungslehre, from which linear algebra is later developed
Timeline_of_mathematics
Capital city of West Pomerania, Poland
writer Alfred Döblin, actress Dita Parlo, mathematician Hermann Günther Grassmann, Roman Catholic priest Carl Lampert, poet Konstanty Ildefons Gałczyński
Szczecin
Property of a mathematical space
0 dimension Point Zero-dimensional space Integer 1 dimension Line Curve Graph (combinatorics) Real number Length 2 dimensions Plane Surface Polygon Net
Dimension
Leibnizian universal language concept
Wellesley MA: A. K. Peters. Fearnley-Sander, Desmond, 1982. "Hermann Grassmann and the Prehistory of Universal Algebra," The American Mathematical Monthly
Characteristica_universalis
Mathematical model of the physical space
termed geometric algebra, unifying Hamilton's quaternions with Hermann Grassmann's algebra and revealing the geometric nature of these systems, especially
Euclidean_geometry
Origin and evolution of the symbols used to write equations and formulas
Bibcode:1939PCPS...35..416D. doi:10.1017/S0305004100021162. S2CID 121466183. H. Grassmann (1862). Extension Theory. History of Mathematics Sources. American Mathematical
History of mathematical notation
History_of_mathematical_notation
Concept in geometry
L.; Zhang, Y.; Li, C.-K. (2005), "Unitarily invariant metrics on the Grassmann space" (PDF), SIAM Journal on Matrix Analysis and Applications, 27 (2):
Angles_between_flats
Theory of algebraic structures in general
Whitehead's early work sought to unify quaternions (due to Hamilton), Grassmann's Ausdehnungslehre, and Boole's algebra of logic. Whitehead wrote in his
Universal_algebra
would be shown on a graph as a point, a zero-dimensional object. A vector, which has a magnitude and direction, would appear on a graph as a line, which
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Concept in geometry
Let ξ i {\displaystyle \xi _{i}} denote the tautological bundle of the Grassmann bundle G i {\displaystyle G_{i}} of rank rk E i {\displaystyle \operatorname
Localized_Chern_class
Geometric object that has length and direction
including Augustin Cauchy, Hermann Grassmann, August Möbius, Comte de Saint-Venant, and Matthew O'Brien. Grassmann's 1840 work Theorie der Ebbe und Flut
Euclidean_vector
Mathematics timeline
Poncelet Geometric properties of the complex projective plane. 1840 Hermann Grassmann General n-dimensional linear spaces. 1848 Carl Friedrich Gauss Pierre
Timeline_of_manifolds
Study of curves from a differential point of view
{\displaystyle {\boldsymbol {\gamma }}(t)=ae^{kt}(\cos {t},\sin {t}).} The first graph to the right shows a logarithmic spiral for values of t from 0 to 13, a
Differentiable_curve
ph; p bh; b b b Greek p, Sanskrit b before any aspirated consonant (Grassmann's law) *dʰ th; t dh; d d d Greek t, Sanskrit d before any aspirated consonant
History_of_Latin
Mathematical function, in linear algebra
{\displaystyle f:\mathbb {R} \to \mathbb {R} :x\mapsto cx} , of which the graph is a line through the origin. More generally, any homothety v ↦ c v {\textstyle
Linear_map
Decomposition in multilinear algebra
Semantic Matching Energy Network (SME) Neural Tensor Networks Recurrent Graph Tensor Networks General polynomial system solving algorithms: homotopy continuation
Tensor_rank_decomposition
Mathematics of smooth surfaces
its isometric embedding in Euclidean space. Surfaces naturally arise as graphs of functions of a pair of variables, and sometimes appear in parametric
Differential geometry of surfaces
Differential_geometry_of_surfaces
Tensor in differential geometry
Notions of Ricci curvature on discrete manifolds have been defined on graphs and networks, where they quantify local divergence properties of edges.
Ricci_curvature
Algebra based on a vector space with a quadratic form
references to Schönberg's papers of 1956 and 1957 as described in section "The Grassmann–Schönberg algebra Gn" of Bolivar 2001 See for ex. Oziewicz & Sitarczyk
Clifford_algebra
Four-dimensional analog of the icosahedron
due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility
600-cell
German award
2005: Joop van den Ende (producer of musical and theatre) 2006: Werner Grassmann (founder of cinema Abaton) 2007: Claus Bantzer (composer and church musician)
Biermann-Ratjen-Medaille
drawings and prints by Clóvis Graciano, Iberê Camargo, Maria Bonomi, Marcelo Grassmann, Poty Lazzarotto, etc. The collection of antiquities at the Ema Klabin
Ema Gordon Klabin Cultural Foundation
Ema_Gordon_Klabin_Cultural_Foundation
GRASSMANN GRAPH
GRASSMANN GRAPH
Girl/Female
American, Australian, Chinese
Flat Grassland
Girl/Female
American, Australian, British, Chinese, Christian, Danish, English, French, German, Indian
Shining Meadow; Bright Grassland; Country Meadow; Bright Meadow
Girl/Female
American, Australian, Indonesian
Bright Grassland
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
English (chiefly Lancashire)
English (chiefly Lancashire) : nickname from Middle English fitten ‘lying’, ‘deceit’ (of unknown origin).English (chiefly Lancashire) : possibly a habitational name from Fitton Hall in Cambridgeshire, named in Anglo-Scandinavian as ‘settlement (Old English tūn) on the fit (Old Norse fit)’, a term denoting grassland on the bank of a river.
Surname or Lastname
English
English : topographic name for someone who lived by a stone cross, from Old Norse kross (see Cross 1) + Middle English man.Altered spelling of German Crossmann or Crössmann; the first may be a habitational name from any of several places called Crossen in Saxony, Brandenburg, and East Prussia, or derived from Grossmann. The second is possibly from Middle Low German krÅs, krüs ‘pitcher’, and hence a metonymic occupational name for maker of these; alternatively it may be a metonymic occupational name for a butcher, from Middle High German kroese ‘tripe’.
Surname or Lastname
German (Grassmann)
German (Grassmann) : elaborated form of of Grass 1 and 4.English : occupational name for a seller of grease, from Old French graisse, greisse, gresse ‘grease’.English : occupational name from Middle English grasman, gresman ‘cottager’, from Middle English gras, gres ‘grass’, ‘pasture’ + man.
Girl/Female
American, British, English
Bright Meadow; Bright Grassland
Surname or Lastname
English, German (Passmann), and Jewish (Ashkenazic)
English, German (Passmann), and Jewish (Ashkenazic) : variant of Pass.
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Boy/Male
Italian Spanish
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
Surname or Lastname
German (also Gräff), Dutch, and Jewish (Ashkenazic)
German (also Gräff), Dutch, and Jewish (Ashkenazic) : variant of Graf.English : metonymic occupational name for a clerk or scribe, from Anglo-Norman French grafe ‘quill’, ‘pen’ (a derivative of grafer ‘to write’, Late Latin grafare, from Greek graphein).
Boy/Male
Spanish American Italian Latin
Enduring. The poet Dante Alighieri wrote The Divine Comedy with its graphic description of...
GRASSMANN GRAPH
GRASSMANN GRAPH
Girl/Female
Hindi Sanskrit
Named for the Lalita Vistara.
Girl/Female
Sikh
Entertaining, Pleasing
Boy/Male
Bengali, Hindu, Indian
Sun Ray
Boy/Male
Tamil
Manishith | மாஂநீஷித
Desired, Loved
Girl/Female
Hindu
New, ***
Boy/Male
Hindu, Indian
Respect
Girl/Female
American, Australian, British, Christian, English, Greek, Jamaican, Latin
Star; Esther; Stella; Inspiring
Boy/Male
Tamil
Yashaswin | யஷஸà¯à®µà®¿à®¨Â
Successful boy
Boy/Male
Arabic Muslim
Stubborn.
Girl/Female
Hindu, Indian
The Light of the Lamp
GRASSMANN GRAPH
GRASSMANN GRAPH
GRASSMANN GRAPH
GRASSMANN GRAPH
GRASSMANN GRAPH
a.
Pertaining to, containing, derived from, or resembling, graphite.
n.
See Graphoscope.
adv.
In a graphic manner; vividly.
a.
Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer.
n.
An instrument which, when applied over an artery, indicates graphically the movements or character of the pulse. See Sphygmogram.
n.
An instrument for recording graphically the variations of temperature, or the indications of a thermometer.
a.
Resembling graphite or plumbago.
n.
A chart or graphic representation of the average distribution of rain over the surface of the earth.
n.
The quality or state of being graphic.
a.
Alt. of Graphitoidal
n.
A pen-shaped pointing device used to specify the cursor position on a graphics tablet.
n.
Alt. of Graphicalness
n.
Anything which represents graphically a succession of events, states, or acts; as, an historical map.
n.
A crucible; as, a graphite pot; a melting pot.
n.
Same as Graphite.
n.
Hence, any graphic or vivid delineation or description of a person; as, a portrait in words.
a.
Alt. of Graphical
n.
An instrument for measuring, and recording graphically, the pressure of the blood in any of the blood vessels of a living animal; -- called also kymographion.
a.
Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula.
n.
A mineral, a telluride of gold and silver, of a steel-gray, silver-white, or brass-yellow color. It often occurs in implanted crystals resembling written characters, and hence is called graphic tellurium.