Web Definition: Linear Algebra
Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces, linear transformations & systems of linear equations. Vector spaces are a central theme in modern mathematics ; thus, linear algebra is widely used in both abstract algebra & functional analysis. Linear algebra also has a concrete representation in analytic geometry. It has extensive applications in the natural sciences & the social sciences. The history of modern linear algebra dates back to the years 1843 & 1844. In 1843, William Rowan Hamilton discovered the quaternions. In 1844, Hermann Grassmann published his book Die lineare Ausdehnungslehre. Linear algebra had its beginnings in the study of vectors in Cartesian 2-space & 3-space. A vector, here, is a directed line segment, characterized by both length or magnitude & direction. Vectors can be used then to represent certain physical entities such as forces & they can be added & multiplied with scalars, thus forming the first example of a real vector space.
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