The definition of matrix multiplication indicates a row-by-column multiplication, where the entries in the i th row of A are multiplied by the corresponding entries in the j th column of B and then adding the results. For instance, the entry a 23 is the entry in the second row and third column.) (The entry in the i th row and j th column is denoted by the double subscript notation a i j, b i j, and c i j. If A = is an m × n matrix and B = is an n × p matrix, the product AB is an m × p matrix.ĪB =, where c i j = a i 1 b 1 j + a i 2 b 2 j+ … + a in b n j. We can only multiply two matrices if their dimensions are compatible, which means the number of columns in the first matrix is the same as the number of rows in the second matrix.
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