Description
Advanced Linear Algebra
Textbooks in Mathematics Series
Author: Woerdeman Hugo
Language: EnglishSubjects for Advanced Linear Algebra:
Keywords
Linearly Independent; Linear Algebra; QR Algorithm; Matrix Theory; Vector Space; Vector Spaces; Jordan Canonical Form; Jordan form; Vector Space V1; Advanced Linear algebra; QR Factorization; Matrix Algebra; Positive Semidefinite; Linear Transformations; Minimal Polynomial; Finite Dimensional Vector Space; Additive Inverse; Finite Dimensional Spaces; Linear Map; Row Reduced Echelon Form; Row Reduction; Jordan Block; Multiplicative Inverse; Tensor Product; Completely Positive Maps; Row Echelon Form; A11b11 A11b12 A12b11 A12b12 A11b21; Anti-symmetric Tensor; Gram Schmidt Process; Partial Matrix; Riemann Hypothesis; Field Axioms
· 15.6x23.4 cm · Hardback
Description
/li>Contents
/li>Biography
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Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author?s emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor products.
Written in clear and concise language, the text sticks to the development of linear algebra without excessively addressing applications. A unique chapter on "How to Use Linear Algebra" is offered after the theory is presented. In addition, students are given pointers on how to start a research project. The proofs are clear and complete and the exercises are well designed. In addition, full solutions are included for almost all exercises.
Fields and Matrix Algebra. Vector Spaces. Linear Transformations. The Jordan Canonical Form. Inner Product and Normed Vector Spaces. Constructing New Vector Spaces from Given Ones. How to Use Linear Algebra. How to Start Your Own Research Project. Answers to Exercises.
Hugo J. Woerdeman, PhD, professor, Department of Mathematics, Drexel University, Philadelphia, Pennsylvania, USA
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