rank of a matrix

It defines firstly the matrix representation of gird and proves that the Rank of simple graph conjunction matrix is a v-1 conjunction matrix and obtains the conjunction matrix of a directed graph of a thermodynamic system fluid grid by analyzing the fluid grid of a thermodynamic system.

首先定义了网络图的矩阵表示，证明了简单图的关联矩阵T的秩Rank（T）为v1，并对热力系统的流体网络图进行了分析，获得热力系统流体网络有向图的关联矩阵。

The nonsingularity and rank of a bounded grey matrix

有界灰矩阵的非奇异性与秩

The existence conditions and definition region of a grey inverse matrix are studied. Additionally, the new concept of grey rank of a bounded grey matrix and its algorithm are proposed and the criteria for constant-full-rank, constant-non-full-rank, conditional-full-rank of a bounded grey matrix are given.

此外，本文又提出有界灰矩阵的灰秩的新概念与算法，建立了有界灰矩阵恒满秩、恒不满秩、条件满秩的判据。

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.

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。

Then we estimate the displacement rank of a matrix's weighted Moore-Penrose inverse.

然后对矩阵的加权Moore -Penrose 逆的位移秩的大小作了估计.