矩阵秩的Sylvester与Frobenius等式问题

The Sylvester and Frobenius Equation Problem of the Matrix's Rank

本文通过线性空间的线性变换讨论了Sylvester与Frobenius不等式取等号的条件,并将它们推广到矩阵多项式中,建立了一类广泛的秩恒等式。

Through the linear transformation of the linear space, this paper discussed the condition of Sylvester and Frobenius inequality taking mark of equality, and by extending them to the matrix polynomial, set up a type of extensive rank identical equation.