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Per Wiki, generalized variance is the determinant of a covariance matrix: https://en.wikipedia.org/wiki/Generalized_variance

I have heard that if the determinant is small, there is strong correlation among the variables. If the determinant is large, there is weak correlation among the variables.

Are there good guidelines as to how to interpret generalized variance? Is generalized variance even useful in practice?

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    $\begingroup$ What you heard is only a faint shadow of the truth, because "small" and "large" depend very strongly on how many variables are involved. $\endgroup$
    – whuber ♦
    Commented Jul 15, 2020 at 12:42
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    $\begingroup$ Usefull in which context? here is a paper using it ... See also stats.stackexchange.com/questions/273236/… and stats.stackexchange.com/questions/421674/… $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jul 15, 2020 at 16:00
  • $\begingroup$ @whuber is there a way to normalize it? $\endgroup$
    – confused
    Commented Jul 16, 2020 at 12:36
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    $\begingroup$ It's better to examine all the eigenvalues. (The determinant is merely their product.) $\endgroup$
    – whuber ♦
    Commented Jul 16, 2020 at 13:21
  • $\begingroup$ @kjetilbhalvorsen as a single metric to measure overall variance/covariance for your variables. $\endgroup$
    – confused
    Commented Jul 17, 2020 at 11:24

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