complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjorungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices....
Complex-Valued Matrix DerivativesIn this complete introduction to the theory of finding derivatives of scalar-, vector-,and matrix-valued functions in..
cabbage123.. 上传于:2016-01-31 粉丝量:1 该文档贡献者很忙,什么也没留下。 下载此文档 Complex-valued_matrix_derivatives 下载积分: 600 内容提示: 文档格式:PDF | 页数:271 | 浏览次数:136 | 上传日期:2016-01-31 07:25:20 | 文档星级: ...
A systematic theory is introduced for finding the derivatives of complex-valued matrix functions with respect to a complex-valued matrix variable and the complex conjugate of this variable. In the framework introduced, the differential of the complex-valued matrix function is used to identify the ...
If Z\in \mathfrak {g} is a left-invariant vector field on G and \phi :U\rightarrow {{\mathbb {C}}} is a local complex-valued function on G then the k-th order derivatives Z^k(\phi ) satisfy \begin{aligned} Z^k(\phi )(p)=\frac{d^k}{ds^k}\big (\phi (p\cdot \exp...
complex-valued matrix. then \(b{b}^\dagger <1\) providing \(|b_{ij}|<\frac{1}{k^\frac{3}{2}}\) for any \(i, j\in \{1,\ ... \ ,k\}\) . proof of lemma a.5 since \(b{b}^\dagger \) is hermitian and $$\begin{aligned} (b{b}^\dagger )_{{i{\overline{j}}...
K and q are a complex-symmetric, matrix-valued and complex-valued function respectively. Setting K=KR+iKI, we assume that KRKI=KIKR, as this fits the application in Section 3, and that there are positive constants λ,Λ,E and p>n such that (2.1)|K(x)|≤λ,|q(x)|<Λ,for anyx...
Complex-Valued Matrix Differentiation: Techniques and Key Results A systematic theory is introduced for finding the derivatives of complex-valued matrix functions with respect to a complex-valued matrix variable and the c... A Hjorungnes,D Gesbert - 《IEEE Transactions on Signal Processing》 被引...
include both W and CW derivatives in the derivative matrix. ie. for f: C^n -> C^m build a m x 2n dim matrix of complex-valued entries holding W and CW derivatives. If f is holomorphic, the CW entries will be 0 in the derivative matrix, and matrix algebra algorithms can ignore tho...
Complex-valued matrix derivatives: with applications in signal processing and communications. Cambridge, United Kingdom: Cambridge University Press; 2011.10.1017/CBO9780511921490Search in Google Scholar 23. Glover, JD, Sarma, MS, Overbye, TJ. Power system. In: Analysis and design. Stamford: Cengage...