Archive
The dot product multiplies each input by its weight and adds the results into a single number. A neuron uses that operation to compute its weighted sum z equals w times x plus the bias b, and that value decides, after the activation, how strongly the neuron fires in response to the data it receives.
A scalar is a single number, a vector an ordered list of numbers, a matrix a two-dimensional table and a tensor the generalisation to any number of dimensions. In a neural network the data enters as vectors and the weights form matrices, so every layer computes z = Wx + b by combining the two.
The mathematics of neural networks rests on three blocks: linear algebra represents data and weights as vectors and matrices, calculus with derivatives and the chain rule lets the network learn through gradient descent, and probability shapes the loss functions. This roadmap walks that path from beginning to end so you know what to study and in what order.
