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The computer is a tool for storage, manipulation, and presentation of data. The data may be numbers, text, or images, but no matter what the data are, they must be coded into a sequence of 0s and 1s. For each type of data, there are several ways of coding that can be used to store the data and specific ways the data may be manipulated.

Most scientific computational problems involve vectors and matrices. It is necessary to work with either the elements of vectors and matrices individually or with the arrays themselves. Programming languages such as Fortran 77 and C provide the capabilities for working with the individual elements but not directly with the arrays. Fortran 95 and higher-level languages such as Octave or Matlab and R allow direct manipulation with vectors and matrices.

There is a variety of computer software available to perform the operations on vectors and matrices discussed in Chapter 11. We can distinguish the software based on the kinds of applications it emphasizes, the level of the objects it works with directly, and whether or not it is interactive. Some software is designed only to perform certain functions, such as eigenanalysis, while other software provides a wide range of computations for linear algebra. Some software supports only real matrices and real associated values, such as eigenvalues.