Publisher's Synopsis
Encyclopaedia of Advances in Linear Algebra and Matrix Theory is intended to provide various new issues and de¬velopments in different areas of Linear Algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Linear algebra is contributing to a number of post-forward problems, including data assimilation, inverse and pa¬rameter estimation problems, PDE-constrained optimization and control, and uncertainty quantification (UQ). The multiparameter equations associated with stochastic PDEs, which are often a bottleneck in computations, can gener¬ally be formulated as tensor equations or huge matrix equations. Advances in these fields could significantly speed up UQ analysis. As for new applications, many of these continue to be provided by industrial problems in science and engineering. Two other topics that are particularly prominent at present are network analysis and big data. In network problems, linear algebra has helped develop and compare measures of important graph properties, such as, centrality and communicability. These advances are having an impact in many areas, including physics, chemistry, biology, engineering and the social sciences. Looking to the future, there are many open questions in matrix analysis and numerical linear algebra for the techniques and applications.
