线性映射方法在矩阵秩中的应用

Using Method of Linear Map to the Rank Theory of Matrix

运用线性映射的概念于矩阵的运算,给出了几个有关矩阵秩的结果的极其简洁的证明.

Let A is a n×m matrix.A linear map is defined by φ_A∶x a Ax were x is a n-dimension vector.Then we have the result dim ker φ_A=n-r(A).This method is used to prove some inequality of matrix s rank.