Note on Convenient Matrix Notations in Multivariate Statistical Analysis and in the Theory of Linear Aggregation

THE INTRODUCTION of matrix notation and the use of matrix algebra have led to considerable simplifications in the treatment of those fields which are essentially quantitative, linear, and multivariate. In linear econometrics, for instance, this statement is valid for both of its theoretical constituents, mathematical economics and statistical analysis. The purpose of this note is to give two new contributions to the simplifications mentioned above. The first of these (to be discussed in Section 2) has to do with variances and covariances. Measuring variables as deviations from their arithmetic means is a common procedure in statistics. Until now, however, it has been insufficiently realized that there exists a matrix corresponding to this linear transformation, the use of which may be profitable in certain mathematical proofs. It can be defined as