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arXiv · 1705.07288

Orthogonality to matrix subspaces, and a distance formula

Priyanka Grover
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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 $\mathbb M_n(\mathbb C)$.

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Priyanka Grover. 2017-05-20. Orthogonality to matrix subspaces, and a distance formula. https://arxiv.org/abs/1705.07288

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