This paper introduces a general version of the information matrix consisting of the autocorrelation and cross-correlationmatrices of the shifted input and output data. Based on the concept of data correlation, a new system realization algorithm was developed to create a model directly from input and output data. The algorithm starts by computing a special type of correlation matrix derived from...

We consider the valence-bond-solid ground state of the q-deformed higher-spin AKLT model (q-VBS state). We investigate the eigenvalues and eigenvectors of a matrix (G matrix), which is constructed from the matrix product representation of the q-VBS state. We compute the longitudinal and transverse spin-spin correlation functions, and determine the correlation amplitudes and correlation lengths ...

A theorem is presented relating the squared multiple correlation of each measure in a battery with the other measures to the unique generalized inverse of the correlation matrix. This theorem is independent of the rank of the correlation matrix and may be utilized for singular correlation matrices. A coefficient is presented which indicates whether the squared multiple correlation is unity or n...

We discuss methods to quantitatively investigate the properties of correlation matrices of a financial system. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Specifically, we discuss how to define and obtain hierarchical trees, correlation-based trees and networks from a correlati...

The simplest way to describe the dependence for a set of financial assets is their correlation matrix. This correlation matrix can be improper when it is specified element-wise. We describe a new method for obtaining a positive definite correlation matrix starting from an improper one. The expert’s opinion and trust on each pairwise correlation is described by a beta distribution. Then, by comb...

(a) Perform a principal components analysis of this dataset on both the covariance and correlation matrices, reporting both estimated variances and loadings. Why are the results different? Why does PCA on the correlation matrix make more sense for this data? The remaining parts assume that you use PCA on the correlation matrix. Solution: The results are different because PCA is not scale invari...