# Simple question related to an ANN diagram showing all of the matrices' dimensions: inputs, weights and output

I've been reading a few Neural Networks articles for the past week and one thing that I am still trying to grasp is the dimensioning of the matrices on an ANN training. I have created a diagram (based on the example given by the same article) to try to figure it out. I have inserted the weights related to the neurons that are painted on the diagram.

I am hoping that someone can validate my reasoning, as it is one of my pain points right now.

I appreciate any help.

PS: Was this post supposed to be created on this forum or on Cross Validated? I can see that this topic appears on both.

Yes. reasoning presented here is correct. Mind that $$x$$ input vector is a row vector (not a column one): $$[x_1, x_2, x_3]$$. Multiplying $$x\cdot w^1$$ provides you an another row vector $$y_1 = [y_{11}, y_{12}, y_{13}, y_{14}]$$ which represents output of neurons 1 to 4 in 1st hidden layer.
Then you multiply $$y_1\cdot w^2$$ and gain another row vector and so on until the outlayer. At last performing an multiplying 1x4 $$\cdot$$ 4x1 provides you a scalar which will be a net output after using output's neuron's transfer function on that scalar.