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

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)

Science & Math

Murota, Kazuo

Sugihara, Masaaki

Mathematics

Wspc/others

Linear Algebra Ii: Advanced Topics For Applications (Utokyo Engineering Course/ Basic Mathematics)

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.

Co-Published with World Scientific

This is the second volume of the two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course. The objective of this second volume is to branch out from the standard mathematical results presented in the first volume to illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volumes covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory. The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest. The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas.

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Books by Sugihara, Masaaki

See the best price to sell, buy, or rent books by Sugihara, Masaaki. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

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

Linear Algebra Ii: Advanced Topics For Applications (Utokyo Engineering Course/ Basic Mathematics)

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

Linear Algebra Ii: Advanced Topics For Applications (Utokyo Engineering Course/ Basic Mathematics)