基本解释：矩阵的秩
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By means of the rank of matrix, line outspreading, it gives some conditions in which a matrix can decompose to two Kronecker products of matrix.对矩阵Kronecker积分解进行研究,通过矩阵的秩,行展开等方法,给出了将一个矩阵分解为两个矩阵Kronecker积的若干条件。
In this note,we describe the equivalent propositions on the rank of matrix by determinants,equivalent of matrix,system of linear equations,linear space,linear mapping and so on.从行列式、矩阵的等价、线性方程组、线性空间、线性映射等角度来刻画矩阵的秩,进而用这些命题来证明与矩阵的秩有关的一些命题。
Necessary and sufficient conditions for the Frobenius inequality of rank of matrix to be equality are dicussed in this paper,and the characterization of rank of a class of matrix is characterized.讨论了矩阵秩的Frobenius不等式取等号的充分必要条件,刻画了一类矩阵的秩特征。
This paper summarizes the applications of elementary transformation of matrix in solving the rank of a matrix or a set of vectors,calculating inverse matrix or system of linear equations,and solving the system of linear equations and the greatest common divisor of polynomials with examples,furthermore,it introduces the thought and application of generalized elementary transformation.文章总结了初等变换在求矩阵的秩、向量组的秩、逆矩阵,求解线性方程组和多项式的最大公因式等方面的应用,并通过实例加以说明,进而介绍了广义初等变换的思想方法和应用。
There are many proofs of this theorem: matrix order equals row order of matrix equals line order of matrix.关于定理"矩阵的秩=矩阵的行秩=矩阵的列秩"的证明方法较多,本文将用初等变换的方法给出证明,此证明方法易于理解,便于计算机编程实现,有利于机器证明。
Based on the equality between the schein rank of matrix and the rank of matrix on Soft Algebra [0,1], this paper constructively demonstrates that the unique generalized inverse matrix exists in any non-zero matrix on [0,1].本文在软代数[0,1]上矩阵的schein秩等于其秩的基础上,构造性地证明了[0,1]上任一非零矩阵都存在唯一的广义逆矩阵。
The Rank and Property of Matrices Over Hermite RingHermite环上矩阵的秩及性质
Rank of the Matrix of the Generalized Fibonacci of the Same Class一类广义Fibonacci矩阵的秩
The Equivalence of the Rank of Linear Transformation And Corresponding Matrix线性变换的秩与其对应矩阵的秩的等价性
The Rank of Sequence of Fibonacci Number {F_n~K}_(k=1)~∞ Matrix;Fibonacci数列{F_n~K}_(k=1)~∞矩阵的秩
A Conclusion and Application of the Ranks of Coprime Polynomial Matrices;互素多项式矩阵的秩的一个简单结论及其应用
Conclusions of matrix order by using lump matrix;利用分块矩阵讨论矩阵秩的几个结论
A Rank Equality of Matrix and the Generalizations of Equality for Involutory Matrices一个矩阵秩恒等式与对合矩阵秩等式的推广
On the Expression of the Block Matrix of the Sum and Product Sequence of Matrix;关于矩阵的和与乘积秩的分块矩阵表示
Using Block-Matrix to Prove a Few Matrix Properties;用矩阵分块方法证明矩阵秩的一些性质
On Characteristics of(m,l)Rank-idempotent Matrix and(m,l)Idempotent Matrix(m,/)秩幂等矩阵和(m,/)幂等矩阵的特性研究
About A Few Declines Arbitrary Formuls Of Matrix Rank As Equivalence;关于矩阵秩的几个降阶公式的等价性
The Modification for an Important Inequality Which is Related to Rank of Matrix;关于矩阵秩的一个重要不等式的改进
Decomposing a Matrix into a Product of Two Full Rank Matrices:an Application of Elementary Matrix Operations初等变换的一个应用:矩阵的满秩分解
The Algorithm of Approximating a Given Matrix with a Hankel Matrix of Lower Rank and Weighted Approximations;低秩Hankel矩阵逼近及其加权逼近的算法
The Sylvester and Frobenius Equation Problem of the Matrix s Rank;矩阵秩的Sylvester与Frobenius等式问题
Ranks of Solutions to Some Quaternion Matrix Equations with Applications若干四元数矩阵方程解的秩及其应用
Notes for a Rank Equality of Matrix and Its Applications关于一个矩阵秩等式的注记及其应用
Full Rank Decomposition and Moore-Penrose Inverses of Completely Symmetric Matrices全对称矩阵的满秩分解及Moore-Penrose逆
