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.
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—except for the zero vector, which is assigned a length of zero.
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 ...
Section "Vector spaces" of chapter ... 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.
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.
Lecture Notes in Mathematics springer
This series reports on new developments in all areas of mathematics and their applications quickly, informally and at a high level. Mathematical texts analysing new developments in modelling and numerical simulation are welcome.
pleteness in Metric or Uniform Spaces Numericana
A metric space is complete when every Cauchy sequence converges in it. Two Cauchy sequences are equivalent when interlacing them yields another Cauchy sequence. The equivalence classes form a complete space.
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
plex numbers, complex analytic functions, Cauchy's integral formula, power series, Liouville's theorem. The maximum modulus theorem.
Linear Algebra from Wolfram MathWorld
Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many other problems in mathematics, physics, and ...