In this paper, using a new method to structure a m-dimensional parallellotope, the geometrical interpretation of the inverse matrix and the generalized inverse of a matrix with full column rank or full row rank are given.
Utilizing the geometrical interpretation of the inverse matrix, we have the following relational volume formulas of parallellotopes for the (ntimes n) real matrices (M,N).
Different intuitive interpretations of the matrices U, Σ, and (V^{T}) are useful in the various domains in which the SVD is applied; here, we focus on right singular vectors as an orthonormal basis for the sentiment time series in the rows of A, which we will refer to as the modes.
Utilizing a new method to structure parallellotopes, a geometrical interpretation of the inverse matrix is given, which includes the generalized inverse of full column rank or a full row rank matrices.
We illustrate some drawbacks to criteria that have been proposed and suggest an alternative, based on the Bayesian interpretation of the alias matrix in Draper and Guttman (Ann. Inst. Statist. Math. 44 (1992) 659).
The remaining elements were easily grouped in two distinct classes after interpretation of the correlation matrix and are: Group 1 = Al, Fe, Co, Ni, As, Cr and Pb, Group 2 = Mn, Zn, Se and Cd, Group 3 = Cu.
This results in a slightly different interpretation of the disambiguation matrix and introduces other small complexities that depend on the way in which the retrieval cue is selected.
As many reactions demonstrated very little variance, further analysis and interpretation of the covariance matrix was aided by removing such reactions.
In the above example, the interpretation of the state transition matrix, is as follows.
The number of components retained was based on interpretation of the factor loading matrix after orthogonal (varimax) rotation and a scree plot (fig 2) that shows the proportion of the variance in total consumption of the food variables.
