# Questions tagged [determinant]

determinant of a matrix. For purely mathematical questions about determinant, better ask at mathSE

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### How to derive the determinant of the variance of a negative multinomial distribution?

The probability mass function of the negative multinomial distribution is: \begin{align*} \mathbb{P}(\boldsymbol{\rm{X}}=\boldsymbol{\rm{x}}|\mathbf{p})=\frac{\Gamma\left(x_0+\sum_{i=1}^{m}x_{i}\right)...
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### Multicollinearity iff determinant correlation matrix = 0

I'm studying Linear Models again, after finishing my degree some years ago. I found in my old notes that, according to my professor, one can check multicollinearity calculating the determinant of the ...
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### Generalized variance of a multivariate normal without calculating determinants

In order to calculate ‘generalized variance’ of a multivariate normal distribution, it is often recommended (e.g., here: https://online.stat.psu.edu/stat505/lesson/1/1.5) to calculate the determinant ...
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### Condition for covariance matrix to be non-invertible

Context: I'm working on a machine learning problem where I'm using multivariate normal likelihood which requires calculating determinant and inverting the covariance matrix. I'm trying to generate ...
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1 vote
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### Impute Missing Correlations from Incomplete Correlation Matrix in R

I am in need of a function that will take an incomplete correlation matrix and return a complete matrix with correlations imputed for missing values. I am working on models that utilize only summary ...
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### How to get the determinant of a covariance matrix from its diagonal elements

I am trying to implement a speaker recognition system in MATLAB. I am using Gaussian Mixture Models (GMM) for speaker modelling and maximizing the posterior probabilities for classification. The ...
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### What does Determinant of Covariance Matrix give?

I am representing my 3d data in covariance matrix. I just want to know what the determinant of a covariance matrix gives. If the determinant is positive, zero, negative, high positive, high negative, ...
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1 vote
2k views

### How to calculate Eigenvalue without using eign() function with R? [closed]

I understand how to calculate EIGN by hand but when I try to write code without function EIGN(), I did not have a clue. To calculate Eigenvalue is to count all the possible c in ...
14k views

### Why do we use the determinant of the covariance matrix when using the multivariate normal?

I am not well versed in statistics. I wanted to know why we use the determinant of the covariance matrix instead of having the covariance matrix itself when writing down the multivariate normal ...
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59k views

### Why does correlation matrix need to be positive semi-definite and what does it mean to be or not to be positive semi-definite?

I have been researching the meaning of positive semi-definite property of correlation or covariance matrices. I am looking for any information on Definition of positive semi-definiteness; Its ...
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### Factor analysis: What to do when determinant is almost zero and when KMO for a variable is low?

I'm conducting a factor analysis on 40 interval-level variables, and have two immediate concerns: The determinant is 6.608E-006, which is much lower than the cut-...
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I am trying to identify the maximum likelihood estimates in an SDM model (a hedonic home price model, with observations being 5,000 individual homes), $$y=\rho W y + X\beta + WX\lambda + \epsilon$$ ...