上三角矩阵

Let R be an arbitrary commutative ring with identity, gl the general linear lie algebra over R consisting of all n × n matricesover R and with the bracket operation = xy -yx, t the lie subalgebraof gl consisting of all n×n upper triangular (resp., strictly upper triangular ) matrices over R and d the lie subalgebra of gl consisting of all n×n diagonal matrices over R.

在第三章中，对R是交换环的情形，讨论了典型李代数的导子代数的结构问题：设R是一个含幺交换环，gl是R上一般线性李代数。t是gl的所有n阶上三角矩阵(相应地，严格上三角矩阵)构成的子代数，d是gl的所有n阶对角阵构成的李代数。

As an application, we also describe the Jordan automorphisms of the algebra of upper triangular matrices over commutative rings, and give a sufficient and necessary condition for a commutative ring being connected.

作为应用，我们还刻划了交换环上的上三角矩阵代数的Jordan自同构，并给出了一个交换环是连通环的充要条件。

The semi singular value decomposition A=USR is suggested,where U is an orthogonal matrix,S is a diagonalizable matrix and R is a upper-triangular matrix.

提出了半奇异值分解A=USR，其中U为正交矩阵，S为对角矩阵，R为上三角矩阵。

Nest algebras are the natural generalizations of upper triangular matrix algebras in infinite dimensional spaces and an important object...

套代数是上三角矩阵代数在无穷维空间上的自然推广，是一类重要的非自伴算子代数。

Nest algebra is an important class of non-selfadjoint reflexive operator algebras, which is the natural generalization of upper triangular matrix algebra in infinite dimensional space.

中文摘要：套代数是一类重要的非自伴、自反算子代数，它是上三角矩阵代数在无穷维空间上的自然推广。

A substance is through the primary transformation into an upper triangular matrix, the transformation matrix is a unit lower triangular matrix.

实质上是将A通过初等行变换变成一个上三角矩阵，其变换矩阵就是一个单位下三角矩阵。

In section one, We characterize when matrix ring, upper triangular matrix ring and trivial extension are simple J-injective rings.

在文章的第一部分我们给出了全矩阵环、上三角矩阵环和平凡扩张是单J—内射环的刻划。

We denote by M_n and T_n the space of n×n full matrices and the space of n×n upper trangular matrices over F, respectively.

设F是域。记M_n和T_n分别为域F上n×n全矩阵空间和n×n上三角矩阵空间。

The algorithm of QR decomposition will be promoted from general Toeplitz matrix to block-Toeplitz matrix.

将一般的Toeplitz矩阵的快速QR分解方法推广到块－Toeplitz矩阵的情形，通过Cholesky方法计算QR分解中的上三角矩阵，并给出了其实现算法。

The HIP algorithm transforms the channel matrix column orthogonally based on Householder transform to avoid the operation of upper triangular matrix and sort the channel matrix only once.

该算法对信道矩阵按列进行Householder正交变换，避免了求上三角矩阵的运算并且仅对信道矩阵进行1次排序。

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。