Computational Linear Algebra

Learn to write programs to solve linear algebraic problems
The Second Edition of this popular textbook provides a highly accessible introduction to the numerical solution of linear algebraic problems. Readers gain a solid theoretical foundation for all the methods discussed in the text and learn to write FORTRAN90 and MATLAB(r) programs to solve problems. This new edition is enhanced with new material and pedagogical tools, reflecting the author's hands-on teaching experience, including:

This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory.

Linear algebra computations using NumPy & SciPy, matrix operations, linear decomposition, principal component analysis

This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving.

Introduction to Computational Linear Algebra presents classroom-tested material on computational linear algebra and its application to numerical solutions of partial and ordinary differential equations.