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language={English}  }  @book{Stewart1973,  author={G W Stewart},  year=1973,  title={Introduction to Matrix Computations},  series={Computer Science and Applied Mathematics},  publisher={Academic Press},  address={Orlando, FL}  }  @book{Hermann1975,  Author = {Robert Hermann},  year = 1975,  diff --git a/section_history.tex b/section_history.tex  index bd31952..9ebc761 100644  --- a/section_history.tex  +++ b/section_history.tex 
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Does Stachey assume integer indexes?  \paragraph{Stewart (1973)~\cite{Stewart1973}}  Vectors come first, but they have distinct columnness. In particular, p. 2:  \begin{quote}  \textbf{Definition 1.1.} A $n$-vector $x$ is a collection of $n$ real numbers  $\xi_1, \xi_2, \dots, \xi_n$ arranged in order in a column:  \[  x = \begin{pmatrix}\xi_1\\\xi_2\\\vdots\\\xi_n\end{pmatrix}.  \]  \end{quote}  p. 21 - Definiion 3.1 An $m\times n$ \textit{matrix} is a rectangualr array of numbers  having $m$ rows and $n$ columns.  p. 21 - Example 3.2. The $n\times1$ matrix $A$ [...] looks exactly like a member of \mathbbR^n. In this book  we shall not distinguish between $n\times1$ matrices and $n$-vectors; they will be denoted by  upper or lower case Latin letters as convenience dictates.  p. 21 - Example 3.3 The $1\times n$ matrix $R$ has the form  \[  R = (\rho_{11},\rho_{12},\dots,\rho_{1n})  \]  Such a matrix will be called a \textit{row vector}  We see here an asymmetry in the indexing conventions between row vectors and  column vectors.  \paragraph{Wirth (1973)~\cite{Wirth1973}}  The book ``Structured Programming'' is possibly the first major textbook on theoretical computer science, as it introduces the study of data structures and algorithms as a discipline separate from mathematics.