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Pel-Recursive Technique
Published in Yun-Qing Shi, Huifang Sun, Image and Video Compression for Multimedia Engineering, 2019
where 〈s→,t→〉 is the inner product between the vector s⇀ and t⇀. Throughout this discussion, when we say vector, we mean column vector. (Row vectors can be handled accordingly.) The inner product is therefore defined as () 〈s⇀,t⇀〉=s⇀t⇀T
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
are called columns of A. An n×m matrix thus consists of n rows and m columns; aij denotes the element or entry, of A in the i th row and j th column. A matrix consisting of just one row is called a row vector whereas a matrix of just one column is called a column vector. The elements of a vector are frequently called components of the vector. When the size of the matrix is clear from the context, we sometimes write A=aij.
Linear Algebra and Matrices
Published in William F. Ames, George Cain, Y.L. Tong, W. Glenn Steele, Hugh W. Coleman, Richard L. Kautz, Dan M. Frangopol, Paul Norton, Mathematics for Mechanical Engineers, 2022
are called columns of A. An n × m matrix thus consists of n rows and m columns; aH denotes the element, or entry, of A in the ith row and jth column. A matrix consisting of just one row is called a row vector, whereas a matrix of just one column is called a column vector. The elements of a vector are frequently called components of the vector. When the size of the matrix is clear from the context, we sometimes write A = (an).
Convergence properties of two networked iterative learning control schemes for discrete-time systems with random packet dropout
Published in International Journal of Systems Science, 2018
Throughout this paper, the notation represents the set of positive integer, i.e. . The symbol refers to the set . T is a given positive integer, , and . is the n-dimensional real column vector space. For , refers to maximum column sum norm defined by .
Sensitivity Coefficient Evaluation of an Accelerator-Driven System Using ROM-Lasso Method
Published in Nuclear Science and Engineering, 2022
Ryota Katano, Akio Yamamoto, Tomohiro Endo
where = M-dimensional column vector= M × N matrix= N-dimensional column vectorT= transpose of a matrix.
Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach
Published in International Journal of Systems Science, 2018
Alireza Nasiri, Sing Kiong Nguang, Akshya Swain, Dhafer Almakhles
Plant Rulei: IF υ1(k) is Ji1 AND ⋅⋅⋅ AND υq(k) is Jiq, THEN where i denotes the ith fuzzy rule (i = 1, …, r); υ1(k), …, υq(k) are the premise variables; q is the number of premise variables and Ji1, …, Jqi are the fuzzy sets. By using a center-average defuzzifier, product inference and singleton fuzzifier, the μi(υ(k)) is defined as where and . The matrices Ai(xk) and Bi(xk) have appropriate dimensions. is a column vector such that , where T(xk) is a polynomial transformation matrix from xk to . Note that, is not unique and gives flexible options to construct the polynomial fuzzy model (4). The model of (4) can be expressed as following: where and .