Sums of squares of matrices (Q1062110)

This paper asks some easily understood matrix questions and gives answers which are equally simple. Indeed, the proofs are also at a level which are within reach of any competent undergraduate. Yet this does not detract from the interest of the paper and also does not mean that some ingenuity was required in finding the proofs. As the author states ''The principal results of this paper are the following: Every integral \(2\times 2\) matrix is the sum of at most 3 integral squares, and this is best possible. Every integral \(n\times n\) matrix with \(n>2\) is the sum of at most k integral squares, where \(k=7\) if n is even, and \(k=9\) if n is odd. Every \(n\times n\) matrix over GF(2) is the sum of at most 2 matrix squares, and this is best possible.'' The paper concludes with a list of interesting open problems.