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invertible matrix

confidence ellipses of bivariate normal distribution

Eigenvalues and eigenvector of a positive-definite, real valued and symmetric matrix

A bivariate normal distributions [BVD] is governed by a central positive symmetric matrix. This matrix is a covariance matrix which describes the variances and correlation of the BVD’s marginal distributions. The contour lines of the probabilty density function of a BVD are ellipses. The half axes and the orientation of these ellipses are controlled by the eigenvalues and eigenvectors of… Read More »Eigenvalues and eigenvector of a positive-definite, real valued and symmetric matrix

Linear transformed 3-dim Z-distribution

Multivariate Normal Distributions – II – Linear transformation of a random vector with independent standardized normal components

In Machine Learning we typically deal with huge, but finite vector distributions defined in the ℝn. At least in certain regions of the ℝn these distributions may approximate an underlying continuous distribution. In the first post of this series we worked with a special type of continuous vector distribution based on independent 1-dimensional standardized normal distributions for the vector components.… Read More »Multivariate Normal Distributions – II – Linear transformation of a random vector with independent standardized normal components