“Hermann Grassmann and the Creation of Linear Algebra”
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Hermann Grassmann
Hermann Günther Grassmann was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. His work preceded and exceeded the concept which is now known as a vector space. He introduced the Grassmannian, the space which parameterizes all k-dimensional li…
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science · German polymath, linguist and mathematician (1809–1877) · mathematician · physicist · linguist · teacher · translator · pedagogue · Indologist · philosopher · also Hermann Grassmann, Hermann Günther Grassmann, Grassmann
Born 15 April 1809 · Died 26 September 1877 · Q77219
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A work on tidal theory... led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the new analysis in such a simple way that the calculations often came out more than ten times shorter than in Lagrange's work.
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1979· 1 entry
1955· 1 entry
A third edition of his dictionary was issued
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1878· 1 entry
William Kingdon Clifford joined this exterior algebra to William Rowan Hamilton's quaternions by replacing Grassmann's rule epep = 0 by the rule epep = 1
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1877· 2 entries
Died 1877-09-26.
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“A work on tidal theory... led me to Lagrange's Mécanique analytique and thereby I returned to those ideas of analysis. All the developments in that work were transformed through the principles of the new analysis in such a simple way that the calculations often came out more than ten times shorter than in Lagrange's work.”
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1876· 1 entry
Received an honorary doctorate from the University of Tübingen
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1875· 1 entry
With a second part of his System according to Grassmann, this time developing higher-dimensional geometry
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1872· 1 entry
Victor Schlegel published the first part of his System der Raumlehre, which used Grassmann's approach to derive ancient and modern results in plane geometry
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1864· 1 entry
As waste paper and the remaining few odd copies have now been sold out, with the exception of the one copy in our library
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1862· 2 entries
Grassmann published a thoroughly rewritten second edition of A1, hoping to earn belated recognition for his theory of extension, and containing the definitive exposition of his linear algebra
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As Die Ausdehnungslehre: Vollständig und in strenger Form bearbeitet (The Extension Theory: Worked out completely and in rigorous form), here referred to as A2
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1861· 1 entry
Grassmann laid the groundwork for Peano's axiomatization of arithmetic in his Lehrbuch der Arithmetik
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1853· 1 entry
Grassmann published a theory of how colors mix; his theory's four color laws are still taught, as Grassmann's laws
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1852· 2 entries
Grassmann was appointed to the former position of his father at Stettin Gymnasium
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Was appointed to his late father's position at the Stettin Gymnasium, thereby acquiring the title of Professor
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1849· 1 entry
Married Therese Knappe and they went on to have eleven children, seven of whom reached adulthood
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1847· 3 entries
The ministry asked Ernst Kummer for a report
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Was made an "Oberlehrer" or head teacher
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Asked the Prussian Ministry of Education to be considered for a university position, whereupon that Ministry asked Ernst Kummer for his opinion of Grassmann
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1846· 2 entries
Möbius invited Grassmann to enter a competition to solve a problem first proposed by Leibniz: to devise a geometric calculus devoid of coordinates and metric properties (what Leibniz termed analysis situs)
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“s 1846 prize essay (see below) contained”
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1844· 2 entries
But Saint-Venant claimed that he had first developed these ideas in 1832
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Grassmann published his masterpiece (A1) commonly referred to as the Ausdehnungslehre, which translates as "theory of extension" or "theory of extensive magnitudes"
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1840· 1 entry
Did so, taking the basic theory from Laplace's Traité de mécanique céleste and from Lagrange's Mécanique analytique, but expositing this theory making use of the vector methods he had been mulling over since 1832
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1834· 1 entry
Grassmann began teaching mathematics at the Gewerbeschule in Berlin, a position previously held by Jakob Steiner
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1830· 1 entry
Studied at Frederick William University Berlin (1827–1830).
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1827· 2 entries
Studied at Marienstiftsgymnasium (1827).
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Studied theology at the University of Berlin, also taking classes in classical languages, philosophy, and literature
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1809· 1 entry
Born 1809-04-15.
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