矩阵在不等式证明中的妙用

On Magical Effect of Matrix in Inequality Proof

矩阵是一种重要的数学方法,在数学领域有其独特的作用。根据正定实对称矩阵的一个重要不等式及均值不等式在矩阵方面的一个重要性质,对国际数学竞赛和不同书刊中有关不等式进行探讨。通过对比,体现了在解某类不等式问题时运用矩阵解题的优势。

Matrix, as an important mathematical means, plays a unique role in various fields of mathematics. On the basis of an important inequality of positive definite real symmetric matrices and a key feature of mean inequality in matrix., some related inequality proof which mentioned in international maths contests and various books are analyzed. By means of contrast, magic effect of matrix is reflected in certain kinds of inequality problems.