A data processing system includes a plurality of general purpose registers, and processor circuitry for executing one or more instructions, including a vector dot product instruction for simultaneously performing at least two dot products. The vector dot product instruction identifies a first and second source register, each for storing a plurality of vector elements, where a first dot product is to be performed between a first subset of vector elements of the first source register and a first subset of vector elements of the second source register, and a second dot product is to be performed between a second subset of vector elements of the first source register and a second subset of vector elements of the second source register. The first and second subsets of the second source register are different and at least two vector elements of the first and second subsets of the second source register overlap.