Taylor expansion for matrix functions of vector variable using the Kronecker product

Nguyen Van Khang, Dinh Cong Dat, Nguyen Thai Minh Tuan
Author affiliations


  • Nguyen Van Khang Hanoi University of Science and Technology, Vietnam
  • Dinh Cong Dat Hanoi University of Mining and Geology, Vietnam
  • Nguyen Thai Minh Tuan Hanoi University of Science and Technology, Vietnam




Taylor expansion, Kronecker product, the partial derivative of a matrix with respect to a vector, elastic manipulator, linearization


Taylor expansion is one of the many mathematical tools that is applied in Mechanics and Engineering. In this paper, using the partial derivative of a matrix with respect to a vector and the Kronecker product, the formulae of Taylor series of vector variable for scalar functions, vector functions and matrix functions are built and demonstrated. An example regarding the linearization of the differential equations of an elastic manipulator is presented using Taylor expansion.


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