ABSTRACT

This chapter presents some elements of linear algebra: the construction of a vector space, the arithmetic of its elements, and the study of a most important class of functions defined over vector spaces. In a vector space, multiplication by a scalar combines a vector with a scalar, to yield another vector. There is no multiplication between two vectors that resembles multiplication between numbers. There is instead the scalar product, which is a binary operation turning a pair of vectors into a scalar. Arithmetic in vector spaces requires a specific set of Maple functions, which belong to the linear algebra library linalg. The function evalm interprets vectors as column vectors. Matrices, like numbers, are algebraic objects, which combine according to two binary operations: addition and multiplication. The Maple implementation is structurally identical to that of any other recursive construction.