In this paper, we explore some algebraic properties of linear structural equation modelsthat can be represented by an HTC-identifiable graph. In particular, we prove that all mixedgraphs are HTC-identifiable if and only if all the regression coefficients can be recovered fromthe covariance matrix using straightforward linear algebra operations. We also find a set ofpolynomials that generates the ideal that encompasses all the equality constraints of the modelon the cone of positive definite matrices. We further prove that this set of polynomials are theminimal generators of said ideal for a subset of HTC-identifiable graphs.

翻译：在本文中,我们探索了线性结构方程模型的一些代数特性,这些模型可以用HTC识别图来表示。特别是,我们证明,所有混合体都是HTC识别的,如果而且只有所有回归系数都可以使用直线直线代数操作从共变矩阵中恢复出来。我们还发现一套极性模型,产生一种理想,它包含模型在正确定矩阵锥形上的所有平等限制。我们进一步证明,这组多义模型是所述理想的极小的生成者,对于HTC识别图子来说。