1) g-orthonormal basis
g-标准正交基
2) orthonormal basis
标准正交基
1.
On the foundation of the conception of orthonormal basis in finite dimensional Euclidean space,this paper provides the theory of completely orthonormal system in infinite dimensional Euclidean space.
从有限维欧氏空间的标准正交基概念出发,构建了无限维欧氏空间的完全规范正交系理论。
2.
Consider the state linear system ∑(A,B,C),If the orthonormal basis _n,n∈N exist in the state space Z,it is proved that the solution of the differential Riccati equation is of general form,i.
考虑状态线性系统∑(A,B,C)中,如果状态空间Z存在一组标准正交基n,n∈N,则微分R iccati方程的解具有形式:∏(t)z=∑nm当n,n∈N是算子A的正规化特征函数时,微分Riccati方程的解有更精确的结果。
3.
In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
在这篇短文中 ,我们证明 :如果 {Φ(x -k) |k ∈Z}是V的界为 1的紧框架 ,那么{Φ(x-k) |k∈Z} 一定是V的一个标准正交
3) normal orthogonal basis
标准正交基
1.
Another method to seek normal orthogonal basis;
标准正交基的另一种求法
2.
By applying elementary transformation,this paper obtains a new method to search for a normal orthogonal basis in Euclid space, it also gives a procedure by which the fewer third elementary transformations are enough to realize this method.
导出用初等变换法求Euclid空间的标准正交基的方法,并进一步获得了只需进行较少次数的第三种类型的初等变换就能实现这一方法的结果。
3.
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.
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。
4) standard orthogonal basis
标准正交基
1.
The fact that each finite subspace has a unique orthogonal in an Eucliden space is proved in virtue of standard orthogonal basis.
文章利用标准正交基,证明了无限维欧氏空间的有限维子空间都有唯一的正交补。
5) standard orthogonal base
标准正交基
1.
The characteristic vector of the real symmetric matrix should be found out, which is orthogonalized and normalized to a standard orthogonal base and is used as row vector to construct the transformation matrix P, so the P~(-1)AP can be made into diagonal matrix.
实对称矩阵A经相似变换P-1AP可化为对角矩阵,在x =Py 下,不一定能化A的二次型为标准型;应寻求对称矩阵A的特征向量,将其正交化并单位化作为标准正交基,作为列向量构造变换矩阵P,可使P-1AP=Λ为对角阵,在x =Py 下,要将二次型化为标准型,且二次项系数即为对角阵Λ主对角线上元素。
6) pseudo-orthonormal basis
伪标准正交基
补充资料:正交基
正交基
orthogonal basis
正交基「“t知艰佣al basis;opToro砚a几‘H曰兹6幻“el 附bert空间X中两两正交的非零元素。,,…,e。,…的系统,使得任一元素x〔X可(唯一地)表成按范数收敛的级数的形式 x=艺c‘e.,该级数称为元素x关于系毛。‘}的Founer级数(Fou-rier series).基{。:}通常选取使得}}e‘l}=1,因而称为规范正交基(orthonorrr以1 basis).这时数c.称为元素x关于规范正交基{。;}的Fo~系数(Fou-rier eoefficients),且取形式c:二(x,e,),一个正交规范系是基的一个必要充分条件是R甘sevai一CTeK加B等式(Parseval一Steklov闪喇ity) 艺I(x,e,)I’=1 tx}l’,对任何x‘X成立.有规范正交基的H正bert空间是可分的,且反之,任何可分Hilbert空间中存在规范正交基.如果任意给定的数系{。,}满足艺,!c.}2<二,则在具有基{。:}的Hilbert空间情况下,级数艺‘c。弓按范数收敛到一个元素x‘X.按此方式任一可分Hilbert空间与空间l:之间建立起一个同构(凡esz-Fisher定理(Riesz一Fisher theorern)).
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