A measure of similarity between two vectors based on their orientation. Two vectors with the same orientation have a cosine similarity of $1$ while two orthogonal vectors have a cosine similarity of $0$, irrespective of their magnitudes. It is derived from the Euclidean dot product formula and is given as: $\text{similarity} = \cos(\theta) = \frac{\mathbf{A}\cdot\mathbf{B}}{||\mathbf {A}|| \ ||\mathbf {B} ||}$. If both vectors $\mathbf{A}$ and $\mathbf{B}$ are normalised, then their magnitudes are both $1$ and the product of their magnitudes ($||\mathbf {A}|| \ ||\mathbf {B} ||$) is also $1$. It therefore follows that, for normalised vectors, the cosine similarity is equal to the dot product between them.