关于实幂等矩阵性质的一些探讨

Research on Some Properties of Real Idempotent Matrices

实矩阵从几何角度理解,可以看作欧氏空间到欧氏空间的线性变换。文章主要利用实矩阵的几何意义,给出了实幂等矩阵一些性质的不同证明,并给出了实对称幂等矩阵的一种刻画。

From the view of geometry, real matrices may be seen as linear transformations on Euclidean spaces. According to the geometric meaning, we give different proofs for some properties of real idempotent matrices, and give a description of the real symmetrical idempotent matrices.