On the Geometry of Subspaces in Euclidean n-Spaces

  title={On the Geometry of Subspaces in Euclidean n-Spaces},
  author={Adi Ben-Israel},
  journal={Siam Journal on Applied Mathematics},
  • Adi Ben-Israel
  • Published 1 September 1967
  • Mathematics
  • Siam Journal on Applied Mathematics

Improved AGSP tools and sub-exponential algorithm for 2D frustration-free uniformly gapped spin systems

We give an improved analysis of approximate ground space projectors in the setting of local Hamiltonians with a degenerate ground space. This implies a direct generalization of the AGSP⇒entanglement

Sharp implications of AGSPs for degenerate ground spaces

We generalize the `off-the-rack' AGSP$\Rightarrow$entanglement bound implication of [Arad, Landau, and Vazirani '12] from unique ground states to degenerate ground spaces. Our condition

On relationships between two linear subspaces and two orthogonal projectors

Abstract Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to

A polynomial-time algorithm for ground states of spin trees

This work is the first to prove an area law and exhibit a provably polynomial-time classical algorithm for local Hamiltonian ground states beyond the case of spin chains.

Formulas for calculating the dimensions of the sums and the intersections of a family of linear subspaces with applications

  • Yongge Tian
  • Mathematics
    Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  • 2019
The union and the intersection of subspaces are fundamental operations in geometric algebra, while it is well known that both sum and intersection of linear subspaces in a vector space over a field

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Let PL denote the orthogonal projector on a subspace L. Two constructions of projectors on intersections of subspaces are given in finite– dimensional spaces. One uses the singular value

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The statistical operation of multiple linear regression by least squares is equivalent to the orthogonal projection of vectors of observations on a space spanned by vectors of observations; and a

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  • R. Penrose
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1956
In an earlier paper (4) it was shown how to define for any matrix a unique generalization of the inverse of a non-singular matrix. The purpose of the present note is to give a further application

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Givenk linear manifolds ℳ1, ..., ℳk and corresponding perpendicular projection matricesP1, ...,Pk, a closed formula is derived for the perpendicular projection matrix with range. The derivation uses

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Sur les matrices qui sont permutables avec leur inverse ggngraliske, Atti

  • Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.,
  • 1963