I'm doing some applied work where I've come across examples that involve real valued square matrices that hold the following property, which expressed using tensor notation is

$$A_{ij}A_{ij} = 1$$

And equivalently with summation notation

$$\sum_{i=1}^N\sum_{j=1}^N A_{ij}*A_{ij}=1$$

Are such matrices known as anything special?

  • 2
    $\begingroup$ Do you mean the Frobenius norm is $1$? $\endgroup$ – A.Γ. Jul 22 '15 at 20:32
  • $\begingroup$ Maybe either matrices that are their own inverses, or square roots of unity/idetntity? $\endgroup$ – Gary. Jul 22 '15 at 20:33
  • $\begingroup$ Are the entries real or complex, or in some other field? $\endgroup$ – Robert Israel Jul 22 '15 at 20:34
  • $\begingroup$ @A.G That indeed matches the operation, so what would it mean to have a Frobenius norm of 1? Seems like there's a related question here $\endgroup$ – jxramos Jul 22 '15 at 20:35
  • $\begingroup$ @RobertIsrael good clarification, they're real valued. $\endgroup$ – jxramos Jul 22 '15 at 20:36

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