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Through the inquiry into the ranks of coprime polynomial matrices,this paper draws a conclusion: Theorem Let f(x),g(x)∈P?眼x?演 and A∈P n×n,if(f(x),g(x))=1,then n+r?眼f(A)g(A)?演=r(f(A))+r(g(A)).

本文给出了互素多项式在矩阵的秩讨论中的一个简单结果:定理:设f(x),g(x)∈P[x],A是n阶方阵,若(f(x),g(x))=1,则n+r[f(A)g(A)]=r(f(A))+r(g(A))。

The direct sum decomposition of the addition of a linear transformation under the coprime polynomial was given,and it was used in the proof of some equality about the rank of idempotent matrix.

给出了两两互素多项式下线性变换的核的直和分解,并应用于幂等矩阵(对合矩阵)的秩的等式证明中。

Using the decompositions of Bezout matrix,resultant matrix and Hankel matrix,the authors get several new properties of these matrices above,which give the matrix expressin of coprime polynomials and supply a new method in dealing with polynomial problems.

利用Bezout矩阵、结式矩阵与Hankel矩阵的分解得到了它们的几个新性质,给出了多项式互素的矩阵描述,为处理多项式问题提供了一种新方法。

The Direct Sum Decomposition of the Addition of a Linear Transformation under the Coprime Polynomial and Its Application;

线性变换在互素多项式下核的直和分解及应用

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

Analysis on accuracy factors of multi-source remote sensing image registration by polynomial model

多源遥感影像多项式配准精度影响因素分析

RESULTS AND PROBLEMS FOR PRIME FACTORIZATIONS MULTIVARIATE POLYNOMIAL MATRICES

多变量多项式矩阵素分解的结果和问题

Gr(?)bner Bases and Primary Decomposition of Ideals and Polynomial Composition

Gr(?)bner基与理想的准素分解及多项式复合

Square Root Algorithm of the Element in Quotient Ring of Rational Coefficient Polynomial Ring

有理系数多项式环的商环中元素的平方根算法

EXISTENCE DETERMINATION AND SOLUTIONG OF THE POLYNOMIAL INVERSE IN REPEAT MODULE POLYNOMIAL RING

重模多项式环中逆元素的存在性判断及求法

Identical Equation of Bernoulli Multinomial and Eurler Multinomial;

有关Bernoulli多项式和Eurler多项式的恒等式

Some Identities on Genocchi Polynomials and Bernoulli Polynomials

关于Genocchi多项式与Bernoulli多项式的恒等式

Multinomial L-regression Analysis on Factors Influencing Elderly-care in Rural Area

农村中青年养老方式影响因素的多项式Logistic回归分析

An expression of two or more terms.

多项式含两个或更多项的一个表达式

Research on Polynomial Functions and Permutation Polynomials;

关于多项式函数与置换多项式的研究

Some properties on the generalized Euler and Bernoulli polynomials;

推广的Euler多项式与Bernoulli多项式的性质

Polynomial Interpolation Based on an Improved Sub-pixel Method of Thickness Measurement of Cable Sheath Material

基于改进的多项式插值亚像素法电缆护套材料厚度测量

Some Identities Involving Bernoulli Polynomials and Euler Polynomials

关于贝努利多项式与欧拉多项式的几个恒等式

compound journal entry

贷借方多项分录式，分项分录式日记帐

Sum of Products of Chebyshev-Gegenbauer L Lengendre Polynomials;

一类包含契贝谢夫多项式—盖根堡多项式—勒让德多项式的积的和

Three Kinds of Symmetric Polynomial Expressed by the Elementary Symmetric Polynomial;

初等对称多项式的多项式表出的三类对称多项式