Linear Algebra I: Basic Concepts (Utokyo Engineering Course/ Basic Mathematics) - Hardcover

Murota, Kazuo; Sugihara, Masaaki

Hardcover

ISBN 10: 9811257027 ISBN 13: 9789811257025

Publisher: WSPC/OTHERS, 2022

Synopsis

This is the first volume of the two-volume book on linear algebra, in the University of Tokyo (UTokyo) Engineering Course. The objective of this volume is to present, from the engineering viewpoint, the standard mathematical results in linear algebra such as those on systems of equations and eigenvalue problems. In addition to giving mathematical theorems and formulas, it explains how the mathematical concepts such as rank, eigenvalues, and singular values are linked to engineering applications and numerical computations. In particular, the following four aspects are emphasized. How matrices arise (discretization of differential equations, description of system structures, description of transition probability) What kinds of matrices arise (sparse matrices, positive definite matrices, diagonally-dominant matrices, nonnegative matrices, integer matrices, polynomial matrices) What characteristics we are interested in (rank, eigenvalues, singular values, positive definiteness) How we can compute (expansion formulas of determinants, elementary transformation, estimates of eigenvalues)

Edition details

• Publisher: WSPC/OTHERS
• Publication date: 2022
• Language: English
• ISBN 10: 9811257027
• ISBN 13: 9789811257025
• Binding: Hardcover
• Number of pages: 314