Vector space A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars. Vector Space from Wolfram MathWorld Vector Space. A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is dimensional Euclidean space, where every element is represented by a list of real numbers, scalars are real numbers, addition is componentwise, and scalar multiplication is multiplication on each term separately. Projective space In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when V = R 2 and V = R 3 are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R 2 denotes ordered pairs of real numbers, and R 3 denotes ordered triplets of ... Axioms | An Open Access Journal from MDPI Axioms (ISSN 2075 1680) is an international peer reviewed open access journal of mathematics, mathematical logic and mathematical physics, published quarterly online by MDPI. A First Course in Linear Algebra Subsection VSP Vector Space Properties. Subsection VS.EVS has provided us with an abundance of examples of vector spaces, most of them containing useful and interesting mathematical objects along with natural operations. 19th Century Mathematics The Story of Mathematics The 19th Century saw an unprecedented increase in the breadth and complexity of mathematical concepts. Both France and Germany were caught up in the age of revolution which swept Europe in the late 18th Century, but the two countries treated mathematics quite differently. Space | Definition of Space by Merriam Webster 7: a set of mathematical elements and especially of abstractions of all the points on a line, in a plane, or in physical space especially: a set of mathematical entities with a set of axioms of geometric character — compare metric space, topological space, vector space