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In my application I am dealing frequently with a multivariate Gaussian distribution of the form $N(\mu,v I)$ where $I$ is an identity matrix, that is, the covariance matrix is just a scalar multiple of the identity matrix.

I keep searching for a name for these kind of multivariate normals which really emphasizes the proprty that the covariance matrix is an identity. There exists the term "spherical" normal, but in this definition we require that the mean is zero.

Is there an accepted nomenclature for this distribution?

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  • $\begingroup$ Uncorrelated Normal Distribution $\endgroup$ – caverac Apr 27 '17 at 15:35
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I think the name you're looking for is "isotropic Gaussian".

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  • 2
    $\begingroup$ @Math_QED it's not a new question, but the answer could do with some elaboration. $\endgroup$ – Glorfindel Jun 16 '17 at 9:17
  • $\begingroup$ I'm gonna edit the answer. $\endgroup$ – njk Jun 16 '17 at 14:40

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