# Square matrix whose sum of squared elements equals 1.

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?

• Do you mean the Frobenius norm is $1$? – A.Γ. Jul 22 '15 at 20:32
• Maybe either matrices that are their own inverses, or square roots of unity/idetntity? – Gary. Jul 22 '15 at 20:33
• Are the entries real or complex, or in some other field? – Robert Israel Jul 22 '15 at 20:34
• @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 – jxramos Jul 22 '15 at 20:35
• @RobertIsrael good clarification, they're real valued. – jxramos Jul 22 '15 at 20:36