# Questions tagged [eigenvalues]

For questions involving calculation or interpretation of eigenvalues or eigenvectors.

415 questions
Filter by
Sorted by
Tagged with
580 views

### General PCA optimization problem

I was looking at the PCA optimization problem, which is finding a matrix $U \in \mathbb{R}^{d\times n}$, $n \le d$, that solves the problem $$\max{tr(U^TCU)},\ \ \ s.t. U^TU = I,$$ where $C$ is the ...
33 views

### What significance can be attached to the eigenmodes of a transition matrix?

I am studying a continuous dynamical system and am categorising preferred areas of the system's phase space using a 3 state hidden Markov model. As the resulting transition matrix is row stochastic, ...
2k views

### Covariance matrix of image data is not positive definite matrix

I've really hit the wall here and need help with direction :). I am trying to use mvnpdf as part of basic EM algorithm but the covariance matrix of data seems to be not positive definite. There are ...
1 vote
187 views

### Rank of N x D vs D x N matrices

If $X$ is a random $N \times D$ matrix where $N > D$, then why is the rank of X - mean(X, 1) $D$ while the rank of ...
4k views

### If the eigenvalues of a covariance matrix have very low variance, what does it mean?

If we have a covariance matrix $A$ $AP=PD$ where $D$ is a diagonal matrix which contains all the eigenvalues then if the variance of the eigenvalues is very small, what does this tell us about $A$? ...
1 vote
77 views

### What should I check after I do PCA?

I have X in which each row is a sample and each column is a predictor. I de-mean X first and then construct the co-variance matrix $A=X^{T}X$ after that I do PCA $AP=PD$ while each column in P is ...
1 vote
214 views

### Why is the result a set of factors instead of just only one?

I am trying to get into SEM and factor analysis. I understand a factor is a latent construct, say e.g. $intelligence$, user-defined by the (weighted) average of a set of indicators $x_1, x_2\dots x_n$....
1 vote
135 views

### Interpreting cointegration test

I am very new to interpreting cointegration tests and eigenvalues, so any help would be appreciated.
267 views

2k views

597 views

### Any intuition for why eigenvector centrality relates to walks of infinite length?

Some centrality measures can be interpreted in terms of walks. Degree centrality relates to a walk of length one: The more walks of length one reach a node, the higher this centrality measure. ...
1 vote
1k views

### Help needed with intuition of eigenvalue spectrum of correlation matrix

I wish to get a better understanding of the meaning of the eigenvalues of a correlation matrix I am studying. I have a correlation matrix of noise levels for 10 cells in a wireless network over time....
222 views

### What happens if I do principal components of the principal components?

Just a hypothetical question: What happens if I do a second principal component analysis over the principal components derived from the first principal component analysis? What will be the ...
1 vote