对称矩阵与Bezout矩阵之间关系的探讨

On Relation between Symmetric Matrix and Bezout Matrix

Bezout矩阵是关于多项式对的一种特殊二次型.首先给出几种特殊情形,随后归纳证明在标准基下,满足条件rank▽A≤2或rankΔA≤2的任意对称矩阵也是Bezout矩阵.在一般基下,任一对称矩阵均可找到由两个多项式生成的Bezou矩阵与之对应.

Bezout matrix is a special quadratic type about a polynomial. This paper firstly gives several special cases and then concludes and proves that,under the standard condition,a discretionary symmetric matrix with rank △↓ A ≤2 or rank ΔA ≤2 is also Bezout matrix and that,under general basis,every symmetric matrix is corresponding to a Bezout matrix with two polynomials.