Fundamentals of linear algebra

著者

• Chahal, J. S.

書誌事項

Fundamentals of linear algebra

J. S. Chahal

（Textbooks in mathematics）

CRC Press, c2019

注記

Includes bibliographical references (p. 221) and index

内容説明・目次

内容説明

Presents theories and applications in an attempt to raise expectations and outcomes The subject of linear algebra is presented over arbitrary fields Includes many non-trivial examples which address real-world problems

目次

Preface Advice to the Reader 1 Preliminaries What is Linear Algebra? Rudimentary Set Theory Cartesian Products Relations Concept of a Function Composite Functions Fields of Scalars Techniques for Proving Theorems 2 Matrix Algebra Matrix Operations Geometric Meaning of a Matrix Equation Systems of Linear Equation Inverse of a Matrix The Equation Ax=b Basic Applications 3 Vector Spaces The Concept of a Vector Space Subspaces The Dimension of a Vector Space Linear Independence Application of Knowing dim (V) Coordinates Rank of a Matrix 4 Linear Maps Linear Maps Properties of Linear Maps Matrix of a Linear Map Matrix Algebra and Algebra of Linear Maps Linear Functionals and Duality Equivalence and Similarity Application to Higher Order Differential Equations 5 Determinants Motivation Properties of Determinants Existence and Uniqueness of Determinant Computational Definition of Determinant Evaluation of Determinants Adjoint and Cramer's Rule 6 Diagonalization Motivation Eigenvalues and Eigenvectors Cayley-Hamilton Theorem 7 Inner Product Spaces Inner Product Fourier Series Orthogonal and Orthonormal Sets Gram-Schmidt Process Orthogonal Projections on Subspaces 8 Linear Algebra over Complex Numbers Algebra of Complex Numbers Diagonalization of Matrices with Complex Eigenvalues Matrices over Complex Numbers 9 Orthonormal Diagonalization Motivational Introduction Matrix Representation of a Quadratic Form Spectral Decompostion Constrained Optimization-Extrema of Spectrum Singular Value Decomposition (SVD) 10 Selected Applications of Linear Algebra System of First Order Linear Differential Equations Multivariable Calculus Special Theory of Relativity Cryptography Solving Famous Problems from Greek Geometry Answers to Selected Numberical Problems Bibliography Index

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB27667769
• ISBN:
  • 9781138590502
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Boca Raton
• ページ数/冊数: xii, 227 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA184.2
  • DC23 : 512/.5
• 件名:
  • LCSH : Algebras, Linear -- Textbooks
• 親書誌ID:
  • BA83550953