J.L.,

Thanks for your prompt reply and your promise of not discouraging.

I knew the reaction would be unbelievable and unacceptable as I said: “我知道这篇小品提出的命题令人难以相信和接受” It is good!

However, could you tell me what was wrong there? May be the Vectors Multiplicative Group does not stand. But why? Or, Is there already an opposite conclusion? I could not find the opposite evidence myself.

Instead, I have found a supporting statement: “一切元在数域F中的n阶可逆矩阵对于矩阵的乘法组成一个群，记作GL_n(F)。” [1]

I translate it as follow:

An n-dimensional reversible matrix, all its elements on field F, makes a multiplicative Group, noted as GL_n(F).  

The Set of reversible matrix includes diagonal matrix. Thus, diagonal matrix is a multiplicative Group. Furthermore, component wise multiplicative vectors is a Group, too. Diagonal matrix is nothing else but an m-vectors. So, all the reasoning comes from the definition of component-wise vectors multiplication. If the component-wise vectors multiplication stands, then just like diagonal matrix, m-vectors is a Group, no doubt. Reversible matrix Є Diagonal matrix, but Diagonal matrix = m-vectors.

In reply, you have mentioned the “big data analysis (大数据分析)”, also in our second meeting back on last September. How do I access Big Data？I don’t know the exact definition of “big data”. But, the stock market data are the “variables-by-samples-by-times data”. It called “three-way-data” by Gauch [2]. It translated into Chinese as Three Subscripts Data, D_(i,j,k), i=1,2,…m, j=1,2,…n, and k=0,1,2,…. , or Crystal Matrix (”三向数据”, “三下标数据”，或”晶阵”). Are they not a “big data”? Or could you tell me where I can get a multivariate time series “Big Data”, other than stock market?  Please keep it in mind that my research is to find the system transition trends T_(k), from existing history data: D_(k)*T_(k)=D_(k+1).

Thank you for your reply rising more valuable discussions.

Have a nice weekend and talk to you later,

Jay, 4/12/2018

[1] 数学手册，高等教育出版社。1979, 第一版，2005年第11次印刷， 北京。465页。

[2] Hugh G. Gauch, Jr. Multivariate analysis in community ecology, Cambridge University Press, 1982, P 69.