两类张量方程解的新表示

对张量ＡＸ＋ＸＡ＝Ｑ，当Ｑ的反对称张量时，该文给出了一个形式对称于Ｑ且只含Ａ和Ｑ低次幂的解。当Ｑ对称或任意张量时，得出了不需计算复杂系数及不含Ａ和Ｑ的高次幂解。对张量方程ＡＸ－ＸＡ＝Ｃ，给出了结构形式和系数都较简单的张量形式妥。最后给出了两类张量方程在计算转动轴和Ｌａｇｒａｎｇｅ旋率的应用实例。

Some New Representations for Solutions of Two Kinds of Tensor Equations

In this paper,for tensor equation AX+ XA=Q,when Q is the skew- symmetric tensor,a simpler solution which is in the symmetric form with respect to Q and lower powers of A and Q is derived.When Q is the symmetric of arbitraty tensor,the solutions to tensor equation are derived,in which we do not need to calculate considerable complicated coefficients and higherpowers of A and Q,For tensor equation AX- XA=C,a solution without considerable complicated coefficients and complicated form is derived. Finally the applications of two kinds of tensor equations are given in determinations of rotation axis and L agrange spin.