论文标题
非交通性多项式的S-周期扩展
Extensions of S-Lemma for Noncommutative Polynomials
论文作者
论文摘要
我们考虑将经典的S-膜从交换案例扩展到非交通案例的问题。我们表明，当且仅当其系数矩阵为正半芬矿时，当对称二次均匀矩阵估计的多项式为正半数时。然后，我们将S-胶成为三种非交通性多项式：非共同多项式的多项式，其系数是实数，基质值的非交通性多项式和遗传性多项式。
We consider the problem of extending the classical S-lemma from commutative case to noncommutative cases. We show that a symmetric quadratic homogeneous matrix-valued polynomial is positive semidefinite if and only if its coefficient matrix is positive semidefinite. Then we extend the S-lemma to three kinds of noncommutative polynomials: noncommutative polynomials whose coefficients are real numbers, matrix-valued noncommutative polynomials and hereditary polynomials.
