Generalizing the angle between a line and a plane in a 3-dimensional Euclidean space,we define the angle between two nontrivial linear manifolds in an ndimensional Euclidean space,which is characterized by a quadratic programming problem with constraints of linear and quadratic equations.Therefore,finding this angle is transformed to solving a non-convex quadratic programming problem.Thus,we present an algorithm for finding this angle,and give a numerical example.We solve the non-convex quadratic programming in this example by means of the Gr(o)bner basis theory.%本文将3维欧氏空间中直线与平面的夹角推广到n维欧氏空间中两线性流形的夹角,并用带线性和二次等式约束的二次规划刻画这个夹角,从而,把求两线性流形夹角的问题转化为求解非凸二次规划问题,由此,给出了计算这种夹角的一个算法和数值算例.在该数值算例中,我们应用Gr(o)bner基理论求解非凸二次规划问题.
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