Vectors, Matrices and Linear Systems

Abstract

The early developments of linear algebra, and related to it those of vectorial analysis, are strongly tied, on the one hand, to the geometrical representation of complex numbers and the need for more abstraction and formalization in geometry and, on the other hand, to the newly developed theory of electromagnetism. The names of William R. Hamilton (1805–1865), August Möbius (1790–1868), Giusto Bellavitis (1803–1880), Adhémar de Saint Venant (1797–1886) and Hermann Grassmann (1808–1877) are connected with the beginning of linear algebra, while J. Willard Gibbs (1839– 1903) and Oliver Heaviside (1850–1925) established the basis of modern vector analysis motivated by the then recent Treatise in Electricity and Magnetism by James Clerk Maxwell (1831–1879). The subsequent formalization is more recent and relates to the developments of functional analysis and quantum mechanics.