Matrix functions of vector variable

Part 1 book "Advanced modern engineering mathematics" includes content: Matrix analysis, numerical solution of ordinary differential equations, vector calculus, functions of a complex variable, laplace transforms.

505p muasambanhan06 03-02-2024 5 1   Download

Part 1 of ebook "Mathematical physics: Applied mathematics for scientists and engineers" provides readers with contents including: Chapter 1 - A review of vector and matrix algebra using subscript/summation conventions; Chapter 2 - Differential and integral operations on vector and scalar fields; Chapter 3 - Curvilinear coordinate systems; Chapter 4 - Introduction to tensors; Chapter 5 - The dirac δ-function; Chapter 6 - Introduction to complex variables; Chapter 7 - Fourier series; Chapter 8 - Fourier transforms; Chapter 9 - Laplace transforms;...

353p lytamnguyet 04-08-2023 9 4   Download

Nonconvex SINR constraints in amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay beamforming problems make the design mathematically intractable. A more practical optimization is to maximize the minimum SINR achievable data rate among all the users. The previously existing methods invoke the vectorization of pre-coding matrix X and then introduce the auxiliary variable matrix of lager dimension which results in an increased computational complexity.

5p viericschmid 12-01-2022 14 2   Download

In this paper, using the definition on partial derivative of a matrix with respect to a vector and Kronecker product [7–9], the formulae of Taylor expansion according to a vector x for scalar functions, vector functions and matrix functions will be built and demonstrated. An applied example regarding the l

12p nguaconbaynhay11 07-04-2021 13 2   Download

In this paper firstly the definitions of partial derivatives of scalar functions, vector functions and matrix functions with respect to a vector variable are represented systematically. After an overview of the matrix calculus related to Kronecker products is presented. Two theorems which specify the relationship between the time derivative of a matrix and its partial derivative with respect to a vector, and the partial derivative of product of two matrices with respect to a vector, are then proved.

11p thienthanquydu 21-10-2018 29 1   Download

part 2 book “essential mathematics for economic analysis” has contents: topics in financial mathematics, functions of many variables, tools for comparative statics, multivariable optimization, determinants and inverse matrices, matrix and vector algebra, linear programming, constrained optimization.

433p tieu_vu13 06-08-2018 37 2   Download