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Proposed $\mathbf{a}\times\mathbf{b}$ for the scalar product and $\mathbf{a}\wedge\mathbf{b}$ for the vector product.  \paragraph{Born and Jordan (1927)}  Explains quantum mechanics as matrix mechanics. First major work to introduce matrices into the physics literature.  They are familiar with the notions of vector analysis, but mainly in 3 and 4 dimensions.  ,,skalare Produkt`` $(\mathfrak A, \mathfrak B)$ (p. 885)  \url{http://link.springer.com.libproxy.mit.edu/article/10.1007/BF01328531}  \paragraph{MacDuffee (1933)~\cite{MacDuffee1933}}  Starts with the abstract axioms of linear algebra and shows that the algebra may be represented by naturally by matrices and matrix multiplication. Also defines array as an ordered set with a known number of elements.