The projections and projection matrices are widely used (see e.g., Basilevsky 1983; Graybill 1983; Horn and Johnson 1990; Lutkepohl 1996). The projections and projection matrices with respect to the symmetric positive definite matrices are often used in algebra and statistics (see e.g., Rao and Mitra 1971; Searle 1982; Harville, 1997; Abadir and Magnus 2005). Harville (1997) discussed in detail the projections and projection matrices with respect to the symmetric positive definite matrices and the projections and projection matrices with respect to the symmetric nonnegative definite matrices. Recently, we found the projection matrices with respect to the symmetric nonnegative definite matrices may be able to be used in linear mixed models (see Wang 2010[9-11]). However, Harville (1997) given the properties of the projection matrices with respect to the symmetric nonnegative definite matrices are not enough. In this paper, we extend the some properties of the projection matrices with respect to the symmetric nonnegative definite matrices. Note that we do not repeat the same properties with his.
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机译：投影和投影矩阵被广泛使用（例如参见Basilevsky 1983; Graybill 1983; Horn and Johnson 1990; Lutkepohl 1996）。关于对称正定矩阵的投影和投影矩阵经常用于代数和统计中（例如参见Rao和Mitra 1971; Searle 1982; Harville，1997; Abadir和Magnus 2005）。 Harville（1997）详细讨论了关于对称正定矩阵的投影和投影矩阵，以及关于对称非负定矩阵的投影和投影矩阵。最近，我们发现关于对称非负定矩阵的投影矩阵可以在线性混合模型中使用（参见Wang 2010 [9-11]）。但是，Harville（1997）给出了相对于对称非负定矩阵的投影矩阵的性质是不够的。在本文中，我们针对对称非负定矩阵扩展了投影矩阵的某些性质。注意，我们不会与他重复相同的属性。
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