Euclidean space/Related Articles

See also changes related to Euclidean space, or pages that link to Euclidean space or to this page or whose text contains "Euclidean space".

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• Banach space [r]: A vector space endowed with a norm that is complete. ^[e]
• Basis (linear algebra) [r]: A set of vectors that, in a linear combination, can represent every vector in a given vector space or free module, and such that no element of the set can be represented as a linear combination of the others. ^[e]
• Bernhard Riemann [r]: German mathematician (1826-1866) notable for differential geometry, function theory, and number theory. ^[e]
• Bounded set [r]: A set for which there is a constant C such that the norm of all elements in the set is less than C. ^[e]
• Cauchy-Schwarz inequality [r]: The inequality $\textstyle (\sum _{i}x_{i}y_{i})^{2}\leq (\sum _{i}x_{i}^{2})(\sum _{i}y_{i}^{2})$ or its generalization |⟨x,y⟩| ≤ ||x|| ||y||. ^[e]
• Compact space [r]: A toplogical space for which every covering with open sets has a finite subcovering. ^[e]
• Complete metric space [r]: Property of spaces in which every Cauchy sequence converges to an element of the space. ^[e]
• Coulomb's law [r]: An inverse-square distance law, like Newton's gravitational law, describing the forces acting between electric point charges; also valid for the force between magnetic poles. ^[e]
• Curl [r]: A vector operator that describes the rotation of a vector field. ^[e]
• Displacement current [r]: Time derivative of the electric displacement D; Maxwell's correction to Ampère's law. ^[e]
• Divergence [r]: A first order differential vector operator acting on a vector field resulting in a scalar function. ^[e]
• Dot product [r]: A type of vector multiplication in Euclidean spaces which produces a scalar result. ^[e]
• Dyadic product [r]: The tensor product between two vectors of the same dimension. ^[e]
• Electric field [r]: force acting on an electric charge—a vector field. ^[e]
• Electromagnetic wave [r]: A change, periodic in space and time, of an electric field E(r,t) and a magnetic field B(r,t); a stream of electromagnetic waves, referred to as electromagnetic radiation, can be seen as a stream of massless elementary particles, named photons. ^[e]
• Euclid's Elements [r]: Mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. ^[e]
• Field (disambiguation) [r]: Add brief definition or description
• Field (mathematics) [r]: An algebraic structure with operations generalising the familiar concepts of real number arithmetic. ^[e]
• Heine–Borel theorem [r]: In Euclidean space of finite dimension with the usual topology, a subset is compact if and only if it is closed and bounded. ^[e]
• Helmholtz decomposition [r]: Decomposition of a vector field in a transverse (divergence-free) and a longitudinal (curl-free) component. ^[e]
• Hilbert space [r]: A complete inner product space. ^[e]
• Identity matrix [r]: A square matrix with ones on the main diagonal and zeroes elsewhere: the identity element for matrix multiplication. ^[e]
• Inner product space [r]: A vector space that is endowed with an inner product and the corresponding norm. ^[e]
• Lorentz force [r]: Force on an electrically charged particle that moves through a magnetic and an electric field. ^[e]
• Magnetic field [r]: Add brief definition or description
• Magnetic induction [r]: Add brief definition or description
• Measure (mathematics) [r]: Add brief definition or description
• Neighbour-sensing model [r]: Add brief definition or description
• Nonlinear programming [r]: Add brief definition or description
• Polar coordinates [r]: Add brief definition or description
• Polarizability [r]: Add brief definition or description
• Rigid motion [r]: Add brief definition or description
• Rotation matrix [r]: Add brief definition or description
• Square circle [r]: Add brief definition or description
• Stokes' theorem [r]: Add brief definition or description
• Tangent space [r]: Add brief definition or description
• Vector field [r]: Add brief definition or description
• Work [r]: Add brief definition or description