两实对称矩阵乘积特征值的上下界

Upper and Lower Bound of Eigenvalues for Multiplication of Two Real Symmetric Matrices

受两实对称矩阵之和特征值的上下界启发,研究了两实对称矩阵乘积特征值的上下界问题.对于两对称正定、对称正定与对称不定、两对称不定且可换的情形,给出了其乘积矩阵特征值的上下界,所得结果与两实对称矩阵之和特征值的上下界有某些相似之处.

Motivated by upper and lower bound of eigenvalues of sum of two real symmetric matrices, we invesetigate upper and lower bound problem of eigenvalues problem of eigenvalues of its multiplication. For the cases of two real symmetric positive definite matrices, one real symmetric positive definite matrix and one real symmetric indefinite matrix, two real symmetric indefinite matrices and commutable, upper and lower bound of eigenvalues of its multiplication are obtained, which are similar to the result of eigenvalues of its sum.