element-wise operator to scale rows of matrix with entries of a vector

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SA-W 2023-1-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1895525-element-wise-operator-to-scale-rows-of-matrix-with-entries-of-a-vector

编辑： Matt J 2023-1-17

Given a matrix and a vector

A = [2 3 4 5;5 4 3 2;1 2 3 4;4 3 2 1];
d = [1 2 3 4];

I want to scale the rows of A with the corresponding entries of d to obtain

res = [2 3 4 5;10 8 6 4;3 6 9 12;16 12 8 4];

I figured out that

res=A.*d(:); --> correct
res2=A.*d; --> wrong, results in column-wise scaling

I know that .* indicates element-wise operations and d(:) re-shapes d into a column-vector, but my question is how to systematically read the expression A.*d(:) . Also, applies the element-wise operator .* to its left argument (here, A) or to its right argument (here, d)?

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Answer 1

Matt J 2023-1-17

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1895525-element-wise-operator-to-scale-rows-of-matrix-with-entries-of-a-vector#answer_1150475

编辑：Matt J 2023-1-17

在 MATLAB Online 中打开

Also, applies the element-wise operator .* to its left argument (here, A) or to its right argument (here, d)?

.* has two operands A and d, so it applies to both of them. It is also commutative (as you would expect), so you could have also done,

res=d(:).*A

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SA-W 2023-1-17

编辑：SA-W 2023-1-17

在 MATLAB Online 中打开

Nice to know these properties.

If the element-wise operator .* has two operands, the elements of the left and right operand are somehow defined. Here, the elements of d are simply the entries, but an element of A could be a row, a column, or a individual entry...I think my question boils down to the following: Given the expression

res=d(:).*A

, how do I know that this expression scales the rows of A?