## 18 Citations

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

- MathematicsBeiträge 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…

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

- Mathematics
- 2020

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

- Mathematics
- 2020

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

- MathematicsSpecial Matrices
- 2019

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

- Computer Science
- 2019

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

- MathematicsBeiträge 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

- Mathematics
- 2013

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

- MathematicsComput. Math. Appl.
- 2013

### Subspaces, angles and pairs of orthogonal projections

- Mathematics
- 2008

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

- MathematicsNumer. Linear Algebra Appl.
- 2006

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…

## References

SHOWING 1-10 OF 11 REFERENCES

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

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1957

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…

### On best approximate solutions of linear matrix equations

- MathematicsMathematical 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…

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

- Mathematics
- 1967

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

- MathematicsJACM
- 1966

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

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

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