关于Hadamard矩阵部分行子阵列的线性无关性

On the linearly independent column vectors of row submatrix of Hadmard matrix

从２阶Ｈａｄａｍａｒｄ矩阵Ｈ＿２经ｍ－１次Ｋｒｏｎｅｒｃｋｅｒ乘积可以得到一个２￣ｍ阶Ｈａｄａｍａｒｄ矩阵Ｈ＿２￣ｍ。该文指出Ｊ．Ｓｒｉｖａｓｔａｖａ的问题等价于从这个２￣ｍ阶Ｈａｄａｍａｒｄ矩阵Ｈ＿２￣ｍ中寻找一个由Ｎ行组成的子阵Ａ＊，使得Ａ＊的行数Ｎ最小而任意ｔ列在实数域上都线性无关。对正整数ｔ，２≤ｔ≤３和２￣（ｍ－１）≤ｔ≤２￣ｍ给出了要使Ａ＊的任意ｔ列都线性无关，Ａ＊必须具有的最小行数，同时给出了矩阵Ａ＊的构造法。

We can obtain Hadamard matrix H_2￣m of order2￣m from a Hadamard matrix of order 2 by(m-1) times of Kronercker product. In this paper we consider the linearindependent of col-umn vectors of row submatrix A* of H_2￣m. For positive integers t,and m with 2≤t≤3 and2￣m-1≤t≤2￣m, we have found the minimum number of rows of A* such that any t columns of A* are linearly independen.We have also presented the method of constructfon forA*.