High Quality Content by WIKIPEDIA articles! In linear algebra, a row vector or row matrix is a 1 x n matrix. The set of all row vectors forms a vector space which is the dual space to the set of all column vectors. Ludwik Silberstein used row vectors for spacetime events; he applied Lorentz transformation matrices on the right in his Theory of Relativity in 1914 (see page 143). In 1963 when McGraw-Hill published Differential Geometry by Heinrich Guggenheimer of the University of Minnesota, he uses the row vector convention in chapter 5, "Introduction to transformation groups" (eqs. 7a,9b and 12 to 15).

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