论文标题
真正的Schur规范和Hadamard矩阵
Real Schur norms and Hadamard matrices
论文作者
论文摘要
We present a preliminary study of Schur norms $\|M\|_{S}=\max\{ \|M\circ C\|: \|C\|=1\}$, where M is a matrix whose entries are $\pm1$, and $\circ$ denotes the entrywise (i.e., Schur or Hadamard) product of the matrices.我们表明，如果这样的矩阵M是n-by-n，则其Schur Norm由$ \ sqrt {n} $界定，并且当且仅当它是Hadamard矩阵时，相等性。我们开发了一种计算SCHUR规范的数值有效方法，作为结果的应用，我们提出了几乎几乎是Hadamard矩阵，这些矩阵比以前已知。
We present a preliminary study of Schur norms $\|M\|_{S}=\max\{ \|M\circ C\|: \|C\|=1\}$, where M is a matrix whose entries are $\pm1$, and $\circ$ denotes the entrywise (i.e., Schur or Hadamard) product of the matrices. We show that, if such a matrix M is n-by-n, then its Schur norm is bounded by $\sqrt{n}$, and equality holds if and only if it is a Hadamard matrix. We develop a numerically efficient method of computing Schur norms, and as an application of our results we present several almost Hadamard matrices that are better than were previously known.
