#REDIRECT [[Quasi-isometry]]
28 bytes (2 words) - 10:09, 17 December 2017
...{A}\right) = B$, that is, if $f$ is a bijection, then $f$ is said to be an isometry from $A$ onto $B$, and $A$ and $B$ are said to be in isometric corresponden
An isometry of real Banach spaces is an affine mapping. Such a linear isometry is realized by (and called) an [[Isometric operator|isometric operator]].
2 KB (277 words) - 06:49, 14 January 2017
If the isometry of surfaces implies congruence, more exactly, if any surface $ F $
...ty that the isometry is necessarily represented by a restriction of a self-isometry of the ambient space, then $ F _ {0} $
2 KB (264 words) - 22:13, 5 June 2020
corresponding under the isometry is less than $ \pi $,
...This fact has enabled one to reduce in a number of cases the study of the isometry of $ F _ {1} $
3 KB (390 words) - 17:45, 4 June 2020
See also [[Quasi-isometry|Quasi-isometry]].
1 KB (212 words) - 08:09, 6 June 2020
quasi-isometry.
...sometry. Some authors (see, e.g., [[#References|[a3]]]) use the word quasi-isometry to denote a mapping having the property above, with the further condition t
3 KB (411 words) - 08:09, 6 June 2020
which is a [[Quasi-isometry|quasi-isometry]] invariant of the [[Metric space|metric space]] $ ( G,d _ {A} ) $,
3 KB (362 words) - 09:44, 14 April 2024
...orms (in another terminology, isometry) and, correspondingly, isomorphism (isometry) of Hermitian spaces (in particular, automorphism). All automorphisms of a
...d isometry of two non-degenerate Hermitian forms over $R$ is equivalent to isometry of the quadratic forms over $R_0$ generated by them; this reduces the class
5 KB (831 words) - 17:13, 9 October 2016
...of a single preserved distance for some mapping $f$ implies that $f$ is an isometry (cf. [[#References|[a1]]]).
...} ^ { 2 }$ to $\mathbf{R} ^ { 3 }$ preserving unit distance necessarily an isometry (cf. [[#References|[a17]]])?
8 KB (1,153 words) - 16:46, 1 July 2020
...nometry is called a dimetry, and if three distortion indices are equal, an isometry; if all distortion indices are different, it is called a trimetry. The prin
1 KB (194 words) - 16:56, 7 February 2011
is an isometry (cf. [[Isometric operator|Isometric operator]]) on a Hilbert space $ {\ma
an isometry on $ {\mathcal H} $
6 KB (815 words) - 09:51, 26 March 2023
...s with respect to completion, which is a more general concept than that of isometry with respect dissection.
4 KB (583 words) - 15:04, 9 April 2014
corresponding in isometry, the trihedra formed by the tangent vectors $ x _ {u} , x _ {v} $
...efore it plays the same part as the rotation indicatrix when examining the isometry of convex surfaces.
4 KB (541 words) - 15:08, 19 January 2021
Any isometry between two subspaces $ F _ {1} $
A second consequence of Witt's theorem may be stated as follows: The isometry classes of non-degenerate symmetric bilinear forms of finite rank over $
4 KB (558 words) - 16:18, 6 June 2020
...the rotation diagrams for these surfaces are the same, and the base of the isometry for the new surfaces has the same spherical image as the original ones. For
In particular, if the base of the isometry for $ S $
4 KB (660 words) - 19:40, 3 January 2021
is a [[Quasi-isometry|quasi-isometry]].
4 KB (659 words) - 08:29, 6 June 2020
.... D. Sullivan introduced the concept of quasi-self-similarity. A $K$-quasi-isometry is defined by a function $f$ acting on a metric space $M$ with metric $d$ s
...ch that multiplication by $1/r$ of $F\cap D_r(x)$ maps into $F$ by a quasi-isometry for all $r<r_0$ and all $x\in F$. (Here $D_r(x)$ is the open ball centred a
4 KB (542 words) - 19:03, 16 April 2014
...{C_{0}}(Y) $. The Banach–Stone theorem asserts that any linear surjective isometry $ T: C(X) \to C(Y) $ is of the form above. Here, if $ X $ is not necessaril
5 KB (819 words) - 17:08, 6 January 2017
and an isometry $ T: V \rightarrow V $.
is the characteristic polynomial of the isometry $ T $.
11 KB (1,631 words) - 17:45, 4 June 2020
...d is locally isometric to the [[Helicoid|helicoid]] and in fact such local isometry can be achieved as endpoint of a continuous one-parameter family of isometr
2 KB (303 words) - 20:07, 12 November 2023