matrixmult

# matrixmult - Math 1b Matrix Multiplication If A has rows ai...

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Math 1b — Matrix Multiplication If A has rows a i and B has columns b j ,then AB has, by deFnition, a i b j as the entry in row i and column j . It is the matrix of dot products. Here are some simple properties and facts about matrix multiplication. These rules follow directly from the deFnition of matrix multiplication. Small examples can help understanding. 1. A (row) vector times a matrix is a linear combination of the rows of that matrix (and the coeﬃcients are the entries of the vector): ( c 1 c 2 ... c ` ) a 1 a 2 . . . a ` = c 1 a 1 + c 2 a 2 + ... + c ` a ` . 2. A matrix times a (column) vector is a linear combination of the columns of that matrix (and the coeﬃcients are the entries of the vector). || | b 1 b 2 b k | c 1 c 2 . . . c k = c 1 | b 1 | + c 2 | b 2 | + + c k | b k | . 3. The rows of the matrix product AB are the rows of A times B . a 1 a 2 . . . a ` B = a 1 B a 2 B . . . a ` B . 4. The columns of AB are A times the columns of B . A | b 1 b 2 b k | = | A b 1 A b 2 ... A b k | . It is clear from this that

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matrixmult - Math 1b Matrix Multiplication If A has rows ai...

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