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

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)?

Answer 1

[Matt J]

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

[SA-W]

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?

[Matt J]

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

Because of Matlab's implicit expansion rules:

So, because d(:) has 1 column and A has N columns, the elements of d(:) get duplicated to form multiple columns before the multiplication is done.