The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The me...The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.展开更多
目的深入刻画线性空间C^(n)与M_(n)中常见的重要的范数的对偶范数。方法利用对偶范数定义及范数的特性,通过Holder不等式、对偶原理、排序不等式、奇异值的Weyl不等式及Neumann不等式进行研究。结果给出C^(n)上l_(p)-范数与k-范数及M_(n...目的深入刻画线性空间C^(n)与M_(n)中常见的重要的范数的对偶范数。方法利用对偶范数定义及范数的特性,通过Holder不等式、对偶原理、排序不等式、奇异值的Weyl不等式及Neumann不等式进行研究。结果给出C^(n)上l_(p)-范数与k-范数及M_(n)上Schatten p-范数和Ky Fan k-范数的表示,并给出M_(n)上算子范数的特性。结论完善了线性空间C^(n)与M_(n)中对偶范数的性质,为利用范数解决数值计算问题奠定了理论基础。展开更多
文摘The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
文摘目的深入刻画线性空间C^(n)与M_(n)中常见的重要的范数的对偶范数。方法利用对偶范数定义及范数的特性,通过Holder不等式、对偶原理、排序不等式、奇异值的Weyl不等式及Neumann不等式进行研究。结果给出C^(n)上l_(p)-范数与k-范数及M_(n)上Schatten p-范数和Ky Fan k-范数的表示,并给出M_(n)上算子范数的特性。结论完善了线性空间C^(n)与M_(n)中对偶范数的性质,为利用范数解决数值计算问题奠定了理论基础。
