Z matrix first row after multiplying A with W[layer 1]

#1

How does X.W give the Z matrix, can you explain to me more? I am unable to understand how the first row became Z1 Z2 Z3 Z4.

#2

Hi, first assume that you have an input of shape (2,3). It means that you have 2 examples and each example has 3 features. Then in hidden layer lets say you have 4 neurons. So the shape of weight matrix will be (3,4).
w=[[w11 w12 w13 w14]
[w21 w22 w23 w24]
[w31 w32 w33 w34]]

Now we are multiplying input*W. It will give us a shape (2,4). Lets say this output matrix is z.
so the z matrix is nothing but matrix multiplication of input and W.
Therefore,
z=[[z11 z12 z13 z14]
[z21 z22 z23 z24]]

For each input example there is corresponding row in z.
Therefore,
z= [[x11 x12 x13] * [[w11 w12 w13 w14]
[x21 x22 x23]] [w21 w22 w23 w24]
[w31 w32 w33 w34]]

So lets picturize z11 now:
z11=x11w11 + x12w21 + x13*w31

Therefore, z[i][j] is nothing but ith example of input(x) * jth column of w.

#3

z= [[x11 x12 x13]] ******** [[w11 w12 w13 w14]

   [x21 x22 x23]]    [w21 w22 w23 w24]

                     [w31 w32 w33 w34]]

Please find the necessary indentation. And instead of multiple **** , it signifies matrix multiplication.

#4

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