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Matrices
Published in Bilal M. Ayyub, Richard H. Mccuen, Numerical Analysis for Engineers, 2015
Bilal M. Ayyub, Richard H. Mccuen
To perform matrix addition, that is, C = A + B, the two or more matrices must have the same number of rows and the same number of columns. The elements of C are then the sum of the corresponding elements of the matrices being summed; that is, cij=aij+bij
Linear Systems
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
Two of the matrix-by-matrix operations defined in linear algebra are matrix addition and multiplication. Matrix addition is the process of adding the corresponding entries of two matrices. This implies that the operation is valid only if the matrices are of the same size. The addition process in the case C = A + B consists of locating each corresponding entry in matrices A and B and storing their sum in the same location in matrix C.
A note on matrix multiplication appearing as element concatenation or coinciding with matrix addition
Published in International Journal of Mathematical Education in Science and Technology, 2022
Samuel B. Allan, Peter K. Dunn, Robert G. McDougall
Students can be asked about other values of r that produce interesting results besides r = 10. One example is when r = 1, when matrix multiplication coincides with matrix addition; for example For the matrix product to coincide with matrix addition, we have no need to ensure all matrix elements are positive integers (so they concatenate) and the solutions can be extended to include negative integers: Here the underlying equation for the result involves matrices A and B such that AB = A + B. That A and B are commutative follows from the proof in the previous section. With the scalar coefficients of A and B both 1 and the commutativity of matrix addition, A and B are interchangeable as well: AB = A + B = B + A = BA. Here, the necessary existence of the matrix is guaranteed for any A and B satisfying the equation. The result is well-established in the literature (for example, Gardner & Wiegandt, 2003, p. 202).