### High, low, and quantitative roads in linear algebra

Robert C. Thompson
1992 Linear Algebra and its Applications
The future of core linear algebra is studied, with attention to advanced tools, elementary devices, and the computer. 1. However, the principal thrust here will be that the core is blended in a significant way with many of the other classifications in Mathematical Reviews, and this will lead to a qualitative prediction. I hope to establish it by adopting a technique sometimes used outside the core but seldom within it: proof by example. LlNEAR ALGEBRA AND ITS APPLICATlONS 162-164:23-64 (1992)
more » ... 0 Elsevier Science Publishing Co., Inc., 1992 655 Avenue of the Americas, New York, NY 10010 0024-3795/92/\$5.00 24 ROBERT C. THOMPSON 2. A QUANTITATIVE PREDICTION An important trend is the increasing availability of good and easily used quantitative tools. This means good and inexpensive computers and good and inexpensive software to run on these wonderful machines. An example is Matlab, in its implementation on personal computers, and Derive, Macsyma, Maple, Mathematics, Milo, and Theorist are some other examples. Matlab provides a beautifully easy command structure for computations involving linear equations, eigenvalues, and singular values, over real and complex scalars, with the hazards from finite precision computer approximations for real numbers kept to a minimum. A future release will include sparse matrix algorithms. Exact integer and multivariable symbolic computations are possible in Derive, Macsyma, Mathematics, Maple, Milo, and Theorist, permitting the testing of conjectures with a ring theory structure. Another useful tool is Galois (for calculations over finite fields), and yet another, for complex variable computations, is appropriately named f(z). Similar software packages are 'The linear and exponential fits, and the graphics, were found using Matlab on a Macintosh Plus. Matlab is published by The Math Works, Inc., South Natick, MA 01760, U.S.A. The root mean square of the deviations from the fit (standard deviation) is about 41.6 for both linear and exponential fits.