CAJ | 학술논문

利用向量组的格拉姆矩阵,给出了欧氏空间中向量组线性无关度的定义,讨论了相关性质,并利用线性无关度给出了向量到子空间的距离公式和非齐次线性方程组最小二乘解的误差公式.据此可以确定一组线性无关度较小的向量组误差最小的线性表示,一个实际例子表明利用向量的线性无关度可以分析一组向量中最重要的向量.
이용향량조적격랍모구진,급출료구씨공간중향량조선성무관도적정의,토론료상관성질,병이용선성무관도급출료향량도자공간적거리공식화비제차선성방정조최소이승해적오차공식.거차가이학정일조선성무관도교소적향량조오차최소적선성표시,일개실제례자표명이용향량적선성무관도가이분석일조향량중최중요적향량.
By using the Gram matrix of vector group,the definition of the degree of linear independence of vector group in the Euclid spacewas given. Some properties are deduced. The distance formula from a vector to a subspace and the error formula of the least square solution ofnon-homogeneous linear equationwere bothpresented in the form of the degree of linear independence. Accordingly,the linear expression with minimum error can be determinedfor a smaller degree of the linearindependence of vector group.A practical exampleshowed that the most importantvector can bechosenby the analysis of degree oflinear independentof vector group.