This paper introduces an extension to the set of Basic Linear Algebra Subprograms (BLAS) aimed at improving the efficiency and portability of matrix-vector operations on high-performance computers. The authors, Jack Dongarra, Jeremy Du Croz, Sven Hammarling, and Richard Hanson, describe the need for an extended set of BLAS routines, particularly for matrix-vector operations, which are frequently used in many linear algebra algorithms. They propose a set of Level 2 BLAS routines that perform operations such as matrix-vector products, rank-one and rank-two updates, and solving triangular equations. These routines are designed to be efficient and modular, and they cover a wide range of matrix types, including general, symmetric, Hermitian, triangular, and band matrices, in both real and complex arithmetic. The paper also discusses naming conventions, argument conventions, storage conventions, and rationale for the proposed extensions. Additionally, it includes appendices detailing the use of full matrix update routines for band matrices and the proposal for extended-precision routines.This paper introduces an extension to the set of Basic Linear Algebra Subprograms (BLAS) aimed at improving the efficiency and portability of matrix-vector operations on high-performance computers. The authors, Jack Dongarra, Jeremy Du Croz, Sven Hammarling, and Richard Hanson, describe the need for an extended set of BLAS routines, particularly for matrix-vector operations, which are frequently used in many linear algebra algorithms. They propose a set of Level 2 BLAS routines that perform operations such as matrix-vector products, rank-one and rank-two updates, and solving triangular equations. These routines are designed to be efficient and modular, and they cover a wide range of matrix types, including general, symmetric, Hermitian, triangular, and band matrices, in both real and complex arithmetic. The paper also discusses naming conventions, argument conventions, storage conventions, and rationale for the proposed extensions. Additionally, it includes appendices detailing the use of full matrix update routines for band matrices and the proposal for extended-precision routines.