Question about the shape of X

Hello, first of all thank you for the course! It really helps me a lot :slight_smile:

The question I want to ask is how the dot product between X and dz can be the row vector of xi*dzi.
Shouldn’t it be a row vector of [x11*dz1 + x21*dz1 + … + xm1*dz1, x12*dz2 + x22*dz2 + … + xm2*dz2, …]?(i wrote xij as i-th element of xj) How can it be [x1*dz1, x2*dz2, x3*dz3, … , xm*dzm]?

Thank you.

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Hello @grimzaeye,

Let me try to show the expanded version of the matrix X, and see if it makes sense to you:

The matrix multiplication in the second line goes like this: take the first row of X, and dot product with the column dz, put the dot product result in the first row of the third line. And repeat this for all rows X.

Note that in the third line, we can see clearly that every pair of element-wise multliplication is about the same sample. For example, x_1^{(1)} won’t be multiplied with dz^{(2)} which are from sample 1 and 2 respectively (note the different number in the superscript). x_i^{(1)} will only be multiplied with dz^{(1)} (note the same number in the superscript).


Oh, I got it.
I misunderstood it like ‘dW(1) = X(1)dZ(1)’
But it should be 'dW(1) = x(1)_1
dz(1) + x(2)_1dz(2) + …+ .x(m)_1dz(m)’ = X(i)_1*dZ

Thank you so much, Raymond.
Have a beautiful day!

No problem :slight_smile: