由此，把复数域上矩阵论的若干重要定理推广到了四元数体。
Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.
特别证明了：在复数域上，几乎所有矩阵都与对角阵相似。
Especially, proved that almost all matrices were similar to diagonal matrices.
探讨了几种复数域的多项式同一性结构，并研究了它们的一些性质。
A few of polynomial identity structures defined on complex field have been discussed and studied.
最后，把菲涅耳数推广到复数域，并用于研究截断高斯光束的衍射问题。
Finally we extend the Fresnel number to the region of complex number, and use it to investigate the diffraction problem of a truncated Gaussian beam.
以瓦特六杆机构为例，在复数域内建立了以角度为变量的复数形式机构分叉分析方程。
Based on a case study of the Watt linkage, the bifurcation equation with Angle variables has been established in complex number field.
本文在复数域上证明了哈密尔顿-凯莱定理，并给出方阵A的特征多项式的全部矩阵根。
The paper proved the Hamilton-Cayley theorem in complex number space, and indicated the all matrix root of the sign multinomial of matrix A.
在复数域内利用分离变量法，得到了这类方程的级数形式的解析解，而最后的解是实数形式。
By using variables separation in the complex number field, the real analytical solution in the form of Fourier series was obtained.
本文将针对无线协同网络着重研究一种物理层网络编码技术—复数域网络编码（CFNC）。
This thesis will focus on research for wireless cooperative networks a physical layer network coding techniques—complex field network coding (CFNC).
在数集的基础上，在整数域上建立了一个新的交换半群，并在有理数域、实数域和复数域上进行了推广；作为应用，讨论了其元素的表示形式。
Based on the number set, a new commutative semi-group is established in the integer number and extended in number fields of rational number, real number and the complex number.
本文提出了一种改进的指纹纹线方向场计算方法，其中重点分析了奇异点模型中旋转角度的估计方法，并在复数域内简化了纹线方向场的优化计算。
This paper introduces an improved algorithm for fingerprint direction field estimation, the rotation angle estimation during constructing the singular point models is analyzed in details.
充分利用二元树复数小波域内系数尺度间和尺度内的统计依赖关系，提出了一种新的局部自适应图像去噪方法。
A new locally adaptive image denoising method, which exploits the intra-scale and inter-scale dependency in the dual-tree complex wavelet domain, is presented.
充分利用二元树复数小波域内系数尺度间和尺度内的统计依赖关系，提出了一种新的局部自适应图像去噪方法。
A new locally adaptive image denoising method, which exploits the intra-scale and inter-scale dependency in the dual-tree complex wavelet domain, is presented.
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