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Matrices
Published in James R. Kirkwood, Bessie H. Kirkwood, Elementary Linear Algebra, 2017
James R. Kirkwood, Bessie H. Kirkwood
A scalar is a number. Scalar multiplication means multiplying a matrix by a number and is accomplished by multiplying every entry in the matrix by the scalar. For example 31−420=3−1260.
Matrices
Published in James R. Kirkwood, Bessie H. Kirkwood, Linear Algebra, 2020
James R. Kirkwood, Bessie H. Kirkwood
A scalar is a number. Scalar multiplication means multiplying a matrix by a number and is accomplished by multiplying every entry in the matrix by the scalar. For example 3(1−420)=(3−1260).
Matrix Algebra
Published in Prem K. Kythe, Elements of Concave Analysis and Applications, 2018
and similarly for BT $ \mathbf{B}^T $ . For addition (or subtraction) of two matrices (A+B $ \mathbf{A}+\mathbf{B} $ , or A-B $ \mathbf{A}-\mathbf{B} $ ) the two matrices A $ \mathbf{A} $ and B $ \mathbf{B} $ must be of equal dimension. Each element of one matrix (B $ \mathbf{B} $ ) is added to (or subtracted from) the corresponding element of the other matrix (A $ \mathbf{A} $ ). Thus, the element b11 $ b_{11} $ in B $ \mathbf{B} $ is added to (or subtracted from) a11 $ a_{11} $ in A $ \mathbf{A} $ ; b12 $ b_{12} $ to (or from) a12 $ a_{12} $ , and so on. Multiplication of a matrix by a number or scalar involves multiplication of each element of the matrix by the scalar, and it is called scalar multiplication, since it scales the matrix up or down by the size of the scalar.
Topological speedups of ℤd-actions
Published in Dynamical Systems, 2022
Aimee S. A. Johnson, David M. McClendon
The reason H is called the first cohomology group comes from the following ideas first studied by Forrest and Hunton [18]. Given a minimal -Cantor system , let be the set of continuous functions from X to . is a -module via usual addition and the scalar multiplication for , . In this context, for an odometer , , the first cohomology group of with coefficients in the module .
UNSCALE: A Fuzzy-based Multi-criteria Usability Evaluation Framework for Measuring and Evaluating Library Websites
Published in IETE Technical Review, 2019
Kokila Harshan Ramanayaka, Xianqiao Chen, Bing Shi
Let two positive triangular fuzzy numbers namely, A= (l1, m1, u1) and B= (l2, m2, u2). The basic fuzzy arithmetic operations on these fuzzy numbers can be defined as [31]: Inverse Addition Subtraction Scalar Multiplication Multiplication Division
Stochastic differential games and inverse optimal control and stopper policies
Published in International Journal of Control, 2019
Tanmay Rajpurohit, Wassim M. Haddad, Wei Sun
Consider the nonlinear stochastic dynamical system given by where, for every t ≥ t0, is a -measurable random state vector, , is an open set with , w(t) is a d-dimensional independent standard Wiener process (i.e. Brownian motion) defined on a complete filtered probability space , x(t0) is independent of (w(t) − w(t0)), t ≥ t0, and and are continuous functions and satisfy f(0) = 0 and D(0) = 0. The filtered probability space is clearly a real vector space with addition and scalar multiplication defined componentwise and pointwise. An -valued stochastic process is said to be a solution of (1) on the time interval [t0, τ] with initial condition if x(·) is progressively measurable (i.e. x(·) is non-anticipating and measurable in t and ω) with respect to the filtration , , , and where the integrals in (2) are Itô integrals.