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..
Patterned Complex-Valued Matrix Derivatives A systematic and simple method is proposed for how to find the derivative of complex-valued matrix functions which depend on matrix arguments that contain ... A Hjorungnes,DP Palomar - Sensor Array & Multichannel Signal Processing Workshop 被引量: 36发表...
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 ...
22.Hjørungnes, A.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...
common_utils import random_fullrank_matrix_distinct_singular_value test_cases1 = ( # some=True (default) # loss functions for complex-valued svd have to be "gauge invariant", # i.e. loss functions shouldn't change when sigh of the singular vectors change. # the simplest choice to ...
. If an operator has an entry in the file derivatives.yaml, then to enable complex backward for that operator, it would have to be added to GRADIENT_IMPLEMENTED_FOR_COMPLEX in gen_variable_type.py. To run a common_methods test for complex, add an entry here: ...
Rarer studies were also presented for cellulose and cellulose derivatives or starch [2a]. Cyclodextrins and calixarenes are good examples of organic host molecules, which can form inclusion complexes with many guest molecules. In a great variety of solid supports, the number and nature of the ...
A differentiable complex function, on the other hand, always has infinitely many derivatives. Here’s another difference: real functions defined through non-singular algebraic expressions are differentiable – which is, however, not true for their complex counterparts. ...
Nonetheless, CDs yield complex valued results and, therefore, they were considered of limited interest in real-world applications. To solve the problem, the conjugated-order differ-integrals were introduced, having complex conjugate derivatives in pairs. In this paper we follow these ideas and apply...