A NOTE ON EFFECT OF OFF-DIAGONAL ENTRIES IN A VARIANCE-COVARIANCE MATRIX ON EIGEN ANALYSIS.

A positive definite symmetric variance covariance matrix with non-zero diagonal entries- plays an important role in multivariate analysis. In this paper we will try to explain the basic algorithm needed to calculate the Eigen values and Eigen vector using such variance covariance matrix (or standardized variance covariance matrix). It is to be noted that coefficients of Principal Components are simply Eigen vectors and Eigen values are there variances (See, Anderson (1984), Johnson &Wichern (1988) &Hotelling (1936)). These eigen values are calculated from variance covariance matrix (or standardized variance covariance matrix). In this paper we will be discussing the effect on eigen analysis when entries in variance covariance matrix are changed. This eigen value problem will be studied on and 3 variance covariance matrix, which then be carried out in higher order matrices (i.e. on 4?4) in order to generalize the coefficients of characteristic polynomial. With some proportion, eigen values vary, when off diagonal entries in variance covariance matrix are changed. This direct or indirect relationship between covariance terms of a variance covariance matrix and its respective eigen values then be deeply studied by regression analysis.