Geometry and the norms of Hadamard multipliers Original Research Article

The norm of a matrix B as a Hadamard multiplier is the norm of the map X → X • B where • is the Hadamard or entrywise product of matrices. We give a geometric interpretation to a criterion of Haagerup and use this interpretation to find an explicit formula for the Hadamard multiplier norms of real 2 × 2 matrices. For Hermitian matrices with one positive eigenvalue, we give necessary and sufficient conditions for the norm to be the magnitude of the largest entry.