Orthogonality to matrix subspaces, and a distance formula
classification
🧮 math.FA
keywords
mathbbdistancematrixobtainbirkhoff-jamesconditionexpressionformula
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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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