Quasi-orthogonal extension of symmetric matrices

An n × n real matrix Q is quasi-orthogonal if Q ⊤ Q = q I n for some positive real number q . If M is a principal sub-matrix of a quasi-orthogonal matrix Q , we say that Q is a quasi-orthogonal extension of M . In a recent work, the authors have investigated this notion for the class of real skew-symmetric matrices. Using a different approach, this paper addresses the case of symmetric matrices.