二次型化标准形常采用配方法，而二次型化标准形等价于它的矩阵合同对角化，文中利用初等矩阵和初等变换之间的关系。
Method of completing square is often used when transforming a quadratic form into a normal one, whose process is equivalent to making the relevant matrix contract diagonal.
利用有限域上一般线性群的BN对分解，给出有限域上的可逆矩阵在置换阵相似变换下的标准形。
We got the standard form of nonsingular matrix over the finite field by means of BN pair decomposition under the similarity transformation of the permutation matrix.
探讨了矩阵标准形在高等代数理论中的若干应用。
This paper probes into some applications of the matrix normal form to advanced algebra theory.
本文讨论赋值环上的对称线性型、二次型和对称矩阵的合同标准形。
In this paper we will discuss symmetric bilinear forms and quadratic forms over valuation rings, and establish the congruent standard forms of symmetric matrices over valuation rings.
借助矩阵的合同变换法，给出了化实二次型为标准形的方法、求标准正交基的方法，并给出了正定二次型判定定理的新证明。
By means of congruent transformation in matrix, the method of transforming real quadratic form into standard form and the method of normal orthogonal basis are given in this paper.
通过实例探讨了实对称矩阵的正交相似变换标准形在矩阵问题中的应用。
Application of standard form of real symmetric matrix under the orthogonal similarity transformation in matrix problems is given by examples.
本文提出了能控标准形和能观测标准形转移矩阵的新求法，并且给出了数学证明。
This paper puts forward a new method of transition matrix for the controllable canonical form and the observable canonical form, and gives a proof in mathematics.
给出了正交矩阵的相似标准形及正交矩阵的分解形式。
This paper describes the orthogonal matrix canonical forms for matrices and the orthogonal matrix decomposition form.
给出了次半正定矩阵的递归判别法，讨论了次半正定矩阵的次合同标准形。
Meanwhile the paper set up a new method to gain the standard form of a real symmetry matrix.
对若当标准形及所使用的可逆矩阵的计算加以简化，并借助若当标准形给出线性递推关系式求解的一般方法。
By using Frobenius matrix, this paper presents the common solution in another form to linear recurrence formula with constant coefficients.
对若当标准形及所使用的可逆矩阵的计算加以简化，并借助若当标准形给出线性递推关系式求解的一般方法。
By using Frobenius matrix, this paper presents the common solution in another form to linear recurrence formula with constant coefficients.
应用推荐