论文标题
某些矩阵的p-norm
The p-norm of some matrices
论文作者
论文摘要
我们计算了一些$ n \ times n $复杂矩阵的操作员$ p $ - norm，可以看作是$ n $ dimensional banach space $ \ ell^p（n）$上的有限线性操作员。定义了对数仿射矩阵的概念，并且对于这样的矩阵，它的$ p $ norm被完全计算。特别是，矩阵$ a = \ begin {pmatrix} 8＆1＆1＆6 \\ 3＆5＆7 \\ 4＆9＆9＆2 \ end eend {pmatrix} $对应于魔术广场，属于魔术广场的类别，属于$ p $ - norm的$ p $ - norm and $ p $ - $ 15 $ $ p \ for not $ p \ forcy for not fory for Infty [1 1，1 1，1。
We compute the operator $p$-norm of some $n\times n$ complex matrices, which can be seen as bounded linear operators on the $n$ dimensional Banach space $\ell^p(n)$. The notion of logarithmic affine matrices is defined, and for such a matrix its $p$-norm is computed exactly. In particular, a matrix $A=\begin{pmatrix} 8 & 1 & 6 \\ 3 & 5 & 7 \\ 4 & 9 & 2 \end{pmatrix}$ which corresponds to a magic square belongs to the class of logarithmic affine matrices, and its $p$-norm is equal to $15$ for any $p\in [1,\infty]$.
