Let A be a 3 by �3 matrix whose eigenvalues are -2, -1 and 2. What is the determinant of the matrix ? Does a matrix and its transpose have the same eigenvectors? Diagonalize the matrix. 3x3 matrix Given matrix A , explain when this matrix can be diagonalized. If A is a matrix...
Of course, the G matrix has very high dimension, and some directions may have zero variance (that is, there may be some zero eigenvalues). Even then, however, the G matrix does not necessarily constrain adaptation in the long term: it inevitably changes as new mutations arise, with effects...
1. Mean centering does not affect the covariance matrix Here, the rational is: If the covariance is the same whether the variables are centered or not, the result of the PCA will be the same. Let’s assume we have the 2 variablesxandy. Then the covariance between the attributes is calcul...
Eigenvectors of matrices with multiple eigenvalues are not unique, or may not even exist. The first matrix C in this case is the identity matrix, I, which is an extreme case for nonuniqueness of eigenvectors. All the eigenvalues are equal to 1, so...
classical PCA reduces the big data dimensionality of extensive MD concatenated trajectories. PC1 and PC2 are the product of the eigenvectors and eigenvalues of the covariance matrix and characterise two orthogonal directions in space along which projections have the most significant variance, interpreted ...
where every node has a unique matrix of graph distance to all other nodes. If such a graph describes the diffusion of information throughout a network, then the maximum “time” (in a number of moves) it could take for information to diffuse throughout the network is when the spanning ...
It can be seen that the orthogonal matrix that transforms 𝑦𝑖yi into 𝑧𝑖zi is none other than the transpose of the matrix whose columns are the normalized eigenvectors of the variance–covariance matrix of the original dataset. When the variables present significantly different variances, ...