be a basis of left-invariant vector fields on $ G $
also constitute a basis of left-invariant vector fields for the Lie subgroup $ H $.
15 KB (2,363 words) - 08:15, 18 August 2022
...he image $\{ p ( t ) : 0 \leq t \leq 1 \}$ of the interval $[0,1]$ under a vector-valued polynomial $p$. The coefficients $a _ { j }$ in that form readily pr
...td> <td valign="top"> G. Farin, "Curves and surfaces for computer aided geometric design" , Acad. Press (1993) (Edition: Third)</td></tr><tr><td valign="to
4 KB (598 words) - 16:55, 1 July 2020
...terior differentiation was developed by Ü. Lumiste [[#References|[a7]]]. A geometric interpretation of the Faddeev–Popov ghost $c$ and anti-ghost $\overline {
It should be noted that all geometric interpretations of the Faddeev–Popov ghosts mentioned above lay aside the
8 KB (1,181 words) - 20:50, 24 January 2021
...athcal{D} ^ { j }$, where $\mathcal{D} ^ { j }$ denotes the [[Vector space|vector space]] of compactly supported differential forms of degree $j$ on $V$ (cf.
See also [[Geometric measure theory|Geometric measure theory]].
5 KB (733 words) - 17:00, 1 July 2020
...lopediaofmath.org/legacyimages/b/b015/b015280/b0152801.png" />-dimensional
vector space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath
...kes it possible to consider the barycentric coordinates of the points of a
geometric complex with respect to all of its vertices. Barycentric coordinates are us
6 KB (811 words) - 17:11, 7 February 2011
...relations between them, on which the definitions of figures are based and geometric propositions are proved, was recognized in the works of even the ancient ge
...the clearness of the drawing and the physical feasibility of the necessary geometric constructions, and were not strictly logically deduced from the axioms and
25 KB (3,631 words) - 19:39, 5 June 2020
$#C+1 = 125 : ~/encyclopedia/old_files/data/V096/V.0906490 Vector measure
or, more generally, a topological vector space). A vector measure $ F $
10 KB (1,436 words) - 09:13, 6 January 2024
...), and linear, bilinear and quadratic functions (functionals and forms) on vector spaces.
...inear transformation, and a linear, bilinear and multilinear function on a vector space.
9 KB (1,394 words) - 08:15, 9 January 2024
One of the basic geometric concepts. A straight line is usually implicitly defined by the axioms of ge
determine the coordinates of the normal vector of this straight line.
2 KB (335 words) - 08:23, 6 June 2020
...of measures, subject to some regularity conditions. Such translation by a vector space of "arrows" is called an affine structure, and it is taken to be th
in terms of its displacement vector $ l ( x, \theta ) $
10 KB (1,420 words) - 08:23, 6 June 2020
...control system defined on a smooth manifold by a pair of smooth admissible vector fields has the strong accessibility property if this pair belongs to some o
...polysystems and control theory" D.Q. Mayne (ed.) R.W. Brockett (ed.) , ''Geometric Methods in System Theory. Proc. NATO Advanced Study Institute, London, Augu
2 KB (329 words) - 15:33, 20 November 2014
...heory]] of the energy function on $\Omega G$ [[#References|[a6]]]. Certain geometric aspects of Birkhoff stratification may be described in terms of non-commuta
...top"> B. Bojarski, "On the stability of Hilbert problem for holomorphic vector" ''Bull. Acad. Sci. Georgian SSR'' , '''21''' (1958) pp. 391–398</td><
4 KB (630 words) - 17:01, 1 July 2020
A generalization of [[Vector analysis|vector analysis]], a part of [[Tensor calculus|tensor calculus]] studying differen
...re general geometric objects than tensor fields, such as tensor densities, vector-valued differential forms, etc. is considered as a part of tensor analysis.
11 KB (1,607 words) - 08:25, 6 June 2020
...respect to area, volume, etc.). The concept of a derivative is extended to vector-valued point functions in an abstract space (see [[Differentiation of a map
For a geometric and mechanical interpretation of the derivative, the simplest rules of diff
4 KB (596 words) - 11:47, 5 July 2016
A topological space associated with a vector (or sphere) bundle or spherical fibration.
be a vector bundle over a CW-complex $ X $.
6 KB (876 words) - 08:25, 6 June 2020
...the [[Parallel displacement(2)|parallel displacement]] of the plane by the vector $ ( a , b ) $,
and parallel displacement by a vector $ ( a , b ) $.
7 KB (1,100 words) - 03:33, 21 March 2022
are the Fourier coefficients of the vector $ f $
The geometric meaning of Bessel's inequality is that the orthogonal projection of an elem
4 KB (620 words) - 04:37, 9 May 2022
is less than one. If in some norm, compatible with the norm of a vector $ x $,
then the simple-iteration method converges at the rate of a geometric series and the estimate
4 KB (568 words) - 20:21, 10 January 2024
...oncept of a CR-manifold (CR-structure) has been defined having in mind the geometric structure induced on a real hypersurface of $ \mathbf C ^ {n} $,
is involutive, i.e., for any complex vector fields $ U $
6 KB (924 words) - 11:07, 26 March 2023
...e _ { k } D _ { k }$ is $\mu$-ample (cf. also [[Ample vector bundle|Ample vector bundle]]).
...B )$ is a Cartier divisor, and let $d$ be the maximum of the dimensions of geometric fibres of $f$. Express $\lambda / r = p / q$ for relatively prime positive
6 KB (873 words) - 09:30, 3 February 2024