On the Geometry of Subspaces in Euclidean n-Spaces

@article{BenIsrael1967OnTG,
  title={On the Geometry of Subspaces in Euclidean n-Spaces},
  author={Adi Ben-Israel},
  journal={Siam Journal on Applied Mathematics},
  year={1967},
  volume={15},
  pages={1184-1198}
}
  • Adi Ben-Israel
  • Published 1 September 1967
  • Mathematics
  • Siam Journal on Applied Mathematics
View via Publisher
benisrael.net
17 Citations
Background Citations
2
Methods Citations
2

17 Citations

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…

Projectors on intersections of subspaces

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…

Perturbations of invariant subspaces of unreduced Hessenberg matrices

Subspaces, angles and pairs of orthogonal projections

We give a new proof for the Wedin theorem on the simultaneous unitary similarity transformation of two orthogonal projections and show that it is equivalent to Halmos' theorem on the unitary…

Jordan's principal angles in complex vector spaces

We analyse the possible recursive definitions of principal angles and vectors in complex vector spaces and give a new projector based definition. This enables us to derive important properties of the…

On the rate of convergence of the alternating projection method in finite dimensional spaces

References

SHOWING 1-10 OF 11 REFERENCES

Orthogonal and oblique projectors and the characteristics of pairs of vector spaces

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…

The Theory of Matrices in Numerical Analysis

On best approximate solutions of linear matrix equations

  • 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…

Contributions to the Theory of Generalized Inverses

Ill-conditioned systems of linear algebraic equations

A generalized inverse ∈-algorithm for constructing intersection projection matrices, with applications

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…

On Error Bounds for Generalized Inverses

On the ``Reverse Order Law'' Related to the Generalized Inverse of Matrix Products

In this paper, some necessary and sufficient conditions for the reverse order property to hold are given.

Generalized Inverses of Partitioned Matrices

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

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