上三角矩阵

If Z is a torsion-free abelian group, then the matrices of L relative to a suitable homogeneous basis of V are uppertriangular.

如果Z是挠自由的群，那么，在V内可选取一组齐次元素组成的基，使得L的矩阵是上三角的。

In chapter three, we study the strongly cleaness of some 3 times3 matrix rings over a commutative local ring and prove that if R is a commutative local ring, Then TM_{3} is a strongly clean ring.

本文第三章主要研究可换局部环上的某些三角矩阵环的强clean 性，并且证明如果 R是可换局部环，则 TM_{3}是强clean矩阵环。

Use Gaussian elimination method to change 'A' into upper triangular matrix.

用高斯消去法改变'甲'到上三角矩阵。

Optimizing and Realization of the Finite Field Inversion Algorithm Based on FPGA;2. The stability and operation of the inversion formula for Toeplitz matrices are also considered.

利用两个线性方程组是否有解给出了Toeplitz矩阵可逆的条件，表明Toeplitz矩阵之逆阵可以表示为φ-循环矩阵与上三角Toeplitz矩阵的乘积之和，给出了其逆矩阵列的递推公式，得到了求Toeplitz矩阵之逆矩阵的快速算法。

In addition, we consider some conditions under which Weyl\'s and Browder\'s theorem hold for operator matrices.In chapter 4, the relationship between the reduced minimum modulus of the left multiplicative operator L_A and the reduced minimum modulus of operator A is discussed.

第三章重点研究了Banach空间上的算子满足Weyl定理和a-Weyl定理，得到了解析余亚正规算子满足a-Weyl定理；同时也讨论了上三角算子矩阵的Weyl(来源：ABC论63文网www.abclunwen.com)定理和Browder定理。

By means of similarity transformation upon the state matrix, an upper triangular matrix or lower triangular matrix is found. The eigenvalues of the original system can be obtained through a series of low-dimension matrixes over the principal diagonal.

该方法对系统状态矩阵进行相似变换，得到分块上三角或下三角矩阵，使原系统特征值可以通过主对角线上一系列相互独立的低维矩阵求得。

The decomposition of the eigenspace of the defective matrix and the general form of Jordan chain ;2. The general form of the maximal Jordan chain s of the defective matrix is getten with the notation of depths of the generalized eigenvectors.

利用广义特征向量的深度，获得极大若当链的一般形式，并推导出在满足PJP-1=SJS-1的2个可逆矩阵P和S之间存在一个主对角线上具有上三角分块Toeplitz子阵的可逆矩阵H，使得S=PH，从而证明广义特征矩阵的唯一性。

In Reference [3], Cao and Tan described the automorphisms of Lie algebra of the strictly upper triangular matrices over R which is a maximal nilpotent subalgebra of the A_n type classical simple Lie algebra.

在参考文献[3]中，曹和谭把由所有严格上三角矩阵所构成的李代数的自同构问题已经完整的解决了，而这样的李代数恰好就是A_n型李代数的一个极大幂零子代数。

The main contents are as follows:(1) Derive recursive Householder transformation formula for transforming the original rectangular matrix column by column into upper triangular matrix, solve the problem of fast upper triangularization of columnvariable matrix.

主要开展的工作有：（1）、导出长方矩阵逐列上三角化的递推Householder变换公式，解决了可变列矩阵的快速上三角化问题。

In chapter 3,we will consider the automorphisms of triangular matrix algebras over commutative semirings.

利用矩阵的一些性质，克服了环上可逆矩阵在半环中未必可逆的难点，证明交换半环R上的n阶三角矩阵代数Tn的自同构都是内自同构。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。