Systems, methods, and apparatuses relating to element sorting of vectors are described. In one embodiment, a processor includes a decoder to decode an instruction into a decoded instruction; and an execution unit to execute the decoded instruction to: provide storage for a comparison matrix to store a comparison value for each element of an input vector compared against the other elements of the input vector, perform a comparison operation on elements of the input vector corresponding to storage of comparison values above a main diagonal of the comparison matrix, perform a different operation on elements of the input vector corresponding to storage of comparison values below the main diagonal of the comparison matrix, and store results of the comparison operation and the different operation in the comparison matrix.