# Summary of Gradient Descent

For a two layer network. The `[]`s denote the layer number.
`'` denotes prime. `T` denotes transpose.

## Scalar implementation

```
dz[2] = a[2] - y
dW[2] = dz[2]a[1]T
db[2] = dz[2]
dz[1] = W[2]Tdz[2] * g[1]'(z[1])
dW[1] = dz[1]xT
db[1] = dz[1]
```


## Vectorized Implementation

```
dZ[2] = A[2] - Y
dW[2] = (1/m)dZ[2]A[1]T
db[2] = (1/m)*np.sum(dZ[2], axis=1, keepdims=True)
dZ[1] = W[2]TdZ[2] * g[1]'(z[1])
db[1] = (1/m)*np.sum(dZ[1], axis=1, keepdims=True)
```