用维数公式证明有关矩阵的(不)等式

Prove Equality and Inequality of the Rank of a Matrix by Dimension Formula

把线性空间中的维数公式推广到一般的矩阵上,并应用它来证明了几个常见的有关矩阵秩的不等式和等式,其证明过程非常简捷。

By extending the dimension formula of linear space to the general matrix with the extended dimension formula, we can prove several common equalities and inequalities of the rand of a matrix.