A generalized tournament matrix M is a nonnegative matrix that satisfies $M+M^t=J-I$, where J is the all ones matrix and I is the identity matrix. In this paper, a characterization of generalized tournament matrices with the same principal minors of orders 2, 3, and 4 is given. In particular, it is proven that the principal minors of orders 2, 3, and 4 determine the rest of the principal minors.

中文翻译：

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具有相同主要未成年人的广义锦标赛矩阵

广义锦标赛矩阵M是满足以下条件的非负矩阵$米+{米}^{吨}=杰-我$，其中J是全一矩阵，I是单位矩阵。在本文中，给出了具有 2、3 和 4 阶相同主要未成年人的广义锦标赛矩阵的特征。特别地，证明了2、3、4阶的主要未成年人决定了其余的主要未成年人。