query: First eigenvector of covariance matrix as the direction of largest variance
positive_passages.docid: 25410
positive_passages.text: What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?
negative_passages.docid: 19244
negative_passages.text: Covariance of a random vector after a linear transformation
negative_passages.docid: 38169
negative_passages.text: Bounds on off-diagonal entries of a correlation matrix
negative_passages.docid: 158716
negative_passages.text: Cholesky versus eigendecomposition for drawing samples from a multivariate normal distribution
negative_passages.docid: 152395
negative_passages.text: Random matrix theory impact on covariance matrix analysis
negative_passages.docid: 92455
negative_passages.text: Orthonormalization of non-hermitian matrix eigenvectors
negative_passages.docid: 88211
negative_passages.text: Generate normally distributed random numbers with non positive-definite covariance matrix
negative_passages.docid: 155765
negative_passages.text: How to derive the covariance matrix of $\hat\beta$ in linear regression?
negative_passages.docid: 51682
negative_passages.text: Covariance matrix explanation
negative_passages.docid: 3401
negative_passages.text: The variance of linear regression estimator $\beta_1$
negative_passages.docid: 109090
negative_passages.text: Inverting non positive definite covariance matrix
negative_passages.docid: 4244
negative_passages.text: How to compute PCA scores from eigendecomposition of the covariance matrix?
negative_passages.docid: 77619
negative_passages.text: Generalizing variance to two dimensions
negative_passages.docid: 56670
negative_passages.text: The intuition behind generalized eigenvectors
negative_passages.docid: 123573
negative_passages.text: Is a sample covariance matrix always symmetric and positive definite?
negative_passages.docid: 158264
negative_passages.text: Rotation of Matrices and their interpretation
negative_passages.docid: 68132
negative_passages.text: Small positive eigenvalues found for a negative definite matrix