CAJ | 학술논문

随着刚体运动分析的日益成熟，四元数理论获得了在诸多领域更为广泛的应用。该文从四元数理论的起源谈起，介绍了四元数矩阵的基本表达和主要性质。依托一般矩阵的分解思路，给出了四元数矩阵的奇异值分解和LU分解过程。因为四元数矩阵不满足乘法交换律，在进行LU分解时借助了高斯消去法。最后，在四元数矩阵分解方法的基础上，对线性方程组解的存在性问题进行了研究，并给出了解存在时的解形式。
수착강체운동분석적일익성숙，사원수이론획득료재제다영역경위엄범적응용。해문종사원수이론적기원담기，개소료사원수구진적기본표체화주요성질。의탁일반구진적분해사로，급출료사원수구진적기이치분해화LU분해과정。인위사원수구진불만족승법교환률，재진행LU분해시차조료고사소거법。최후，재사원수구진분해방법적기출상，대선성방정조해적존재성문제진행료연구，병급출료해존재시적해형식。
With the rigid body motion analysis is increasingly maturing ,four element theory had been ap-plied in many fields .In this paper ,our research starts from the origin of four element theory ,and then the basic expression of four and the main properties of quaternion matrix is introduced .Under the general idea of matrix decomposition ,singular value decomposition and LU decomposition process of quaternion matrix is given .Because quaternion matrix does not satisfy the commutative law of multiplication ,Gauss elimina-tion method was used in LU decomposition process .Finally ,the existence of solutions of linear equations are studied and solution existence form is given based on decomposition of quaternion matrix .