# What do we call a set of Gaussians with the same covariance matrix?

What do we call a set of Gaussian distributions with the same covariance but different means?

Is there a particular term for that?

I mean the Gaussians are like:

$N(\mu_1,\Sigma), N(\mu_2,\Sigma), N(\mu_3,\Sigma)...$

• Do you mean with the same variances and with all covariances between pairs of different variables the same? Mar 17, 2016 at 2:32
• @Glen_b yes, all the same, the only difference is the mean. Mar 17, 2016 at 2:33
• Wait, I thought you were talking about common values within a single $\Sigma$. So the common $\Sigma$ is an arbitrary covariance matrix? Mar 17, 2016 at 2:40
• @Glen_b sorry I misunderstood, yes $\Sigma$ is just an arbitrary covariance matrix. Mar 17, 2016 at 2:42

When different multivariate distributions have the same covariance matrix, you could describe them as having "common covariance structure" or "a common covariance matrix, $\Sigma$".