We've studied that the wide-sense elementary transformation ofamatrix, and illustrated its application in determinant calculation, matrix inversion and the rankofamatrix.
The article discusses rankofamatrix by the solution theorem of system of homogeneous linear equations, and proves several famous inequalities and two propositions on rankofamatrix.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
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A modified ULV updating algorithm. is applied to performing noise subspace tracking. The algorithm does not require rank estimation of the correlation matrix, and estimate directly the noise subspace.