类二元分量函数矩阵定号性的判定与应用

Criteria and its applications for definite-sign property of analogy two-element copponent function matrices

为了寻找新的判定分量函数矩阵定号性的方法和技巧,在给出类二元分量函数矩阵及分量函数为分量正(负)定的定义后,证明了三个新的关于类二元分量函数矩阵定号性的定理,同时还举例说明了这些新定理在分量函数矩阵定号性的判定与广义二次型方法中的应用。理论和实例表明,对类二元分量函数矩阵定号性的判定,这些新结果比Svlvester判据更加方便、有效。

For the purpose that new criteria component function matrices, the conceptions of could be found for definite- sign property analogy two - component matrix, component positive and component-negative are defined in this paper ,and then three new theorems for definite- sign property of analogy two-element component functionmatrices are proved,and a example is also given to indicate applications of these new theorems. The theory and example in this paper shows that these new theorems are more convenient than the Sylveter theorem for definite-sign property of analogy two-element component function matrices.