Introduction to Linear Algebra

Abstract

This chapter introduces widely used concepts about linear algebra in computer science, as well as information about the standard libraries that gather kernels for linear algebra operations, such as the basic linear algebra subprograms (BLAS) and the linear algebra package (LAPACK). The creation and evolution of these libraries is historically contextualized to help the reader understand their relevance and utility. Moreover, dense and sparse linear algebra are explained. The authors describe the levels of the BLAS library, the motivation behind the hierarchical structure of the BLAS library, and its connection with the LAPACK library. The authors also provide a detailed introduction on some of the most used and popular dense linear algebra kernels or routines, such as GEMM (matrix-matrix multiplication), TRSM (triangular solver), GETRF (LU factorization), and GESV (LU solve). Finally, the authors focus on the most important sparse linear algebra routines and the motivation behind the discussed approaches.