Orthogonality of matrices in the Ky Fan $k$-norms
  We obtain necessary and sufficient conditions for a matrix $A$ to be Birkhoff-James orthogonal to another matrix $B$ in the Ky Fan $k$-norms. A characterization for $A$ to be Birkhoff-James orthogonal to any subspace $\mathscr W$ of $\mathbb M(n)$ is also obtained. 
Priyanka Grover
math.FA