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Emergence of the concept of rank in the study of systems of linear equations. (Emergence du concept de rang dans l’étude des systèmes d’équations linéaires.) (French) Zbl 0792.01014

Chabert, Jean-Luc (ed.) et al., Analyse diophantienne et géométrie algébrique. Exposés du Séminaire d’Histoire des Mathématiques de l’Institut Henri Poincaré. Paris: Université Pierre et Marie Curie, Lab. de Mathématiques Fondamentales, Cah. Sémin. Hist. Math., 2. Sér. 3, 159-190 (1993).
The appearance of the concept of rank in the study of the algebraic linear systems is discussed. The author considers various results which involve the rank in the works of Cramer, Euler, Sylvester, Cayley, Baltzer, Trudi, Dogson, Rouché, Smith, Frobenius, Graßmann, Capelli, Garbieri, Peano, Burali-Forti and Steinitz. He also presents the historical development of other main concepts of linear algebra and discusses several results about finite dimensional vector spaces and related fields. The paper includes detailed references of the main primary sources.
For the entire collection see [Zbl 0782.00054].

MSC:

01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
15-03 History of linear algebra
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