  A new condition, the strong inner product property, is introduced and used to
construct sign patterns of row orthogonal matrices. Using this property,
infinite families of sign patterns allowing row orthogonality are found. These
provide insight into the underlying combinatorial structure of row orthogonal
matrices. Algorithmic techniques for verifying that a matrix has the strong
inner product property are also presented. These techniques lead to a
generalization of the strong inner product property and can be easily
implemented using various software.
