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There is a page named "Partial isometry" on Wikipedia
- mathematical functional analysis a partial isometry is a linear map between Hilbert spaces such that it is an isometry on the orthogonal complement of its...7 KB (1,275 words) - 00:14, 10 October 2023
- In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed...17 KB (2,325 words) - 17:04, 22 June 2024
- an isometry when its action is restricted onto the support of A {\displaystyle A} , that is, it means that U {\displaystyle U} is a partial isometry. As...25 KB (4,220 words) - 03:42, 18 May 2024
- complex Hilbert spaces is a canonical factorization as the product of a partial isometry and a non-negative operator. The polar decomposition for matrices generalizes...12 KB (1,543 words) - 22:04, 24 May 2024
- {\displaystyle U} such that U † U = I {\displaystyle U^{\dagger }U=I} (a partial isometry), the ensemble { q i , | φ i ⟩ } {\displaystyle \{q_{i},|\varphi _{i}\rangle...36 KB (5,245 words) - 19:07, 29 June 2024
- {T}}} is the partial isometry that vanishes on the orthogonal complement of U {\displaystyle U} , and A {\displaystyle A} is the isometry that embeds U...34 KB (5,802 words) - 21:53, 28 April 2024
- Moore–Penrose pseudoinverse B+ can be. In that case, the operator B+A is a partial isometry, that is, a unitary operator from the range of T to itself. This can...28 KB (4,600 words) - 02:22, 5 May 2024
- meaning that ee = e and e* = e. Every projection is a partial isometry, and for every partial isometry s, s*s and ss* are projections. If e and f are projections...25 KB (3,600 words) - 02:50, 16 March 2024
- bounded operator M , {\displaystyle \mathbf {M} ,} there exist a partial isometry U , {\displaystyle \mathbf {U} ,} a unitary V , {\displaystyle...86 KB (13,746 words) - 22:21, 16 July 2024
- and 1 − p are Murray–von Neumann equivalent, i.e., there exists a partial isometry u such that p = uu* and 1 − p = u*u. One can easily generalize this...13 KB (1,812 words) - 23:17, 26 March 2024
- operators is equivalent to finding unitary extensions of suitable partial isometries. Let H {\displaystyle H} be a Hilbert space. A linear operator A {\displaystyle...19 KB (3,246 words) - 07:18, 7 February 2024
- graphical representations of specific states, unitary operators, linear isometries, and projections in the computational basis | 0 ⟩ , | 1 ⟩ {\displaystyle...30 KB (2,725 words) - 16:09, 6 February 2024
- belonging to M are called (Murray–von Neumann) equivalent if there is a partial isometry mapping the first isomorphically onto the other that is an element...42 KB (5,905 words) - 00:34, 7 May 2024
- Riemannian manifold (section Isometries)surface is called a local isometry. Call a property of a surface an intrinsic property if it is preserved by local isometries and call it an extrinsic...60 KB (8,581 words) - 18:08, 18 July 2024
- structure of T {\displaystyle T} means that a "truncated" shift is a partial isometry on H {\displaystyle {\mathcal {H}}} . More specifically, let { e 0...5 KB (903 words) - 19:35, 2 December 2023
- In linear algebra, the restricted isometry property (RIP) characterizes matrices which are nearly orthonormal, at least when operating on sparse vectors...6 KB (862 words) - 14:39, 1 March 2023
- V2, K2) be two Stinespring representations of a given Φ. Define a partial isometry W : K1 → K2 by W π 1 ( a ) V 1 h = π 2 ( a ) V 2 h . {\displaystyle...12 KB (2,113 words) - 06:14, 30 June 2023
- quasinormal if and only if in its polar decomposition A = UP, the partial isometry U and positive operator P commute. Given a quasinormal A, the idea...8 KB (1,513 words) - 02:20, 1 March 2023
- kernel of P, clearly UP h = 0. But PU h = 0 as well. because U is a partial isometry whose initial space is closure of range P. Finally, the self-adjointness...4 KB (562 words) - 02:22, 1 March 2023
- are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow...27 KB (4,720 words) - 15:59, 22 May 2024
- matrix right inverse two-sided inverse function inverse image inversion isometry isomorphism 1, 2, 3 characterized by dimension definition of a space with