长沙大学学报
長沙大學學報
장사대학학보
Journal of Changsha University
2015年
5期
4-5,10
,共3页
初等变换%多元函数%极值%实对称矩阵%二次型%标准形%正定性
初等變換%多元函數%極值%實對稱矩陣%二次型%標準形%正定性
초등변환%다원함수%겁치%실대칭구진%이차형%표준형%정정성
elementary transformation%multivariate function%extreme value%real symmetric matrix%quadratic form%standard form%positive definite
首先给出了多元函数极值求解的实对称矩阵法，然后受化二次型为标准形的初等变换法的启发，且根据实对称矩阵与二次型之间的关系，得到实对称矩阵的正定性判定的初等变换法。综合以上方法，得到了多元函数极值的初等变换求解法，并给出了相应的定理性的结论。
首先給齣瞭多元函數極值求解的實對稱矩陣法，然後受化二次型為標準形的初等變換法的啟髮，且根據實對稱矩陣與二次型之間的關繫，得到實對稱矩陣的正定性判定的初等變換法。綜閤以上方法，得到瞭多元函數極值的初等變換求解法，併給齣瞭相應的定理性的結論。
수선급출료다원함수겁치구해적실대칭구진법，연후수화이차형위표준형적초등변환법적계발，차근거실대칭구진여이차형지간적관계，득도실대칭구진적정정성판정적초등변환법。종합이상방법，득도료다원함수겁치적초등변환구해법，병급출료상응적정이성적결론。
In this paper,the method for solving the extreme value of multivariate function through real symmetric matrix is given.Quad-ratic form can be simplied into standard form through elementary transformation method.Inspired by this and according to the relation-ship between the real symmetric matrix and the quadratic form,the elementary transformation method to determine the positive definite of real symmetric matrix is also given.Based on above methods,the elementary transformation method of the extreme value of multiva-riate function is obtained,and corresponding rational conclusions are given.
