Orthogonality to matrix subspaces, and a distance formula

Priyanka Grover

Orthogonality to matrix subspaces, and a distance formula

Functional Analysis 2017-05-23 v1

Authors: Priyanka Grover

Abstract

We obtain a necessary and sufficient condition for a matrix $A$ to be Birkhoff-James orthogonal to any subspace $\mathscr W$ of $\mathbb M_n(\mathbb C)$ . Using this we obtain an expression for the distance of $A$ from any unital $C^*$ subalgebra of $\mathbb M_n(\mathbb C)$ .

Keywords

hadamard matrices distance sets

Cite

@article{arxiv.1705.07288,
  title  = {Orthogonality to matrix subspaces, and a distance formula},
  author = {Priyanka Grover},
  journal= {arXiv preprint arXiv:1705.07288},
  year   = {2017}
}

Comments

12 pages

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