Jiahao Chen Fill out Cauchy references  over 8 years ago

Commit id: b6ee0bd66431f6fb61d0f5489a2cecba130ad4ad

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url = {https://books.google.com/books?id=cHGrfrQVq1oC}  }  @article{Cauchy1847,  author = {Augustin Cauchy},  title = {M\'emoire sur les lieux analytiques},  year = 1847,  pages = {885--887},  journal = {Comptes rendus hebdomadaires des séances de l'Académie des sciences},  volume = 24,  }  @article{Hamilton1847,  author = {William Rowan Hamilton},  title = {On Symbolical Geometry}, 

@article{Cauchy1853,  author = {Augustin Cauchy},  title = {Sur les clefs alg\'ebriques},  journal = {Comptes rendus hebdomadaires des séances de l'Académie des sciences},  pages = {70--76, 129--136},  url = {http://gallica.bnf.fr/ark:/12148/bpt6k90192k/f18.item.zoom}, year = 1853 }  @article{Cayley1855,         

\S. 12 introduces the term ``scalar product'' for the case of parallel vectors (which differs from modern usage by a negative sign).  He does not appear to have introduced the general case of non-parallel vectors.  \paragraph{Cauchy (1847)~\cite{Cauchy1847} - analytical mechanics}  set of $n$ variables is an ``analytic product'' (1847)~\cite{Cauchy1847}}  Credited \todo{by whom?} as the earliest description of $n$-dimensional space.  \begin{quote}  Concevons maintenant que le nombre des variables $x, y, z, \dots$  devienne sup\'erieur \`a trois. Alors chaque syst\`eme des valeurs de  $x, y, z, \dots$ d\'eterminera ce que nous appellerons un \text{point analytique}, dont  ces variables seront les \textit{coordonn\'ees} et, \`a ce point, r\'epondra une  certaine valeur de chaque fonction de $x, y, z \dots$  Nous appellerons encore \textit{droite analytique} un syst\`eme de \textit{points  analytiques} dont les diverses coodonn\'ees e'exprimeront \`a l'aide de  fontions lin\'eares donn\'ees de l'une d'entre elles.  \end{quote}  \paragraph{Sylvester (1850)~\cite{Sylvester1850}}         

\ref{rule:col1} is a special case of the indexing rule where the rank of the  result is the sum of the ranks of the indexes. This indexing rule is used by  some languages such as APL. The history of this rule is discussed in  Sec.~\ref{sec:related}. related work.  It is tempting to generalize \ref{rule:v'1} to arrays of general rank, by  considering $A^\prime$ as the array constructed by reversing all the indexes of