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Record Nr. |
UNINA9910460834003321 |
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Autore |
Penney Richard C. |
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Titolo |
Linear algebra : ideas and applications / / Richard Penney |
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Pubbl/distr/stampa |
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Hoboken, New Jersey : , : Wiley, , 2016 |
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©2016 |
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ISBN |
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Edizione |
[Fourth edition.] |
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Descrizione fisica |
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1 online resource (513 p.) |
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Disciplina |
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Soggetti |
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Algebras, Linear |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di contenuto |
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Linear Algebra; Contents; Preface; Features of the Text; Acknowledgments; About the Companion Website; Chapter 1 Systems of Linear Equations; 1.1 The Vector Space of Matrices; The Space Rn; Linear Combinations and Linear Dependence; What Is a Vector Space?; Why Prove Anything?; Exercises; 1.1.1 Computer Projects; Exercises; 1.1.2 Applications to Graph Theory I; Self-Study Questions; Exercises; 1.2 Systems; Rank: The Maximum Number of Linearly Independent Equations; Exercises; 1.2.1 Computer Projects; Exercises; 1.2.2 Applications to Circuit Theory; Self-Study Questions |
Exercises1.3 Gaussian Elimination; Spanning in Polynomial Spaces; Computational Issues: Pivoting; Exercises; Computational Issues: Counting Flops; 1.3.1 Computer Projects; Exercises; Applications to Traffic Flow; Self-Study Questions; Exercises; 1.4 Column Space and Nullspace; Subspaces; Exercises; Computer Projects; Chapter Summary; Chapter 2 Linear Independence and Dimension; 2.1 The Test for Linear Independence; Bases for the Column Space; Testing Functions for Independence; Exercises; 2.1.1 Computer Projects ; Exercises; 2.2 Dimension; Exercises; 2.2.1 Computer Projects |
Exercises2.2.2 Applications to Differential Equations; Exercises; 2.3 Row Space and the rank-nullity theorem; Bases for the Row Space; Summary; Computational Issues: Computing Rank; Exercises; 2.3.1 Computer Projects; Exercises; Chapter Summary; Chapter 3 Linear Transformations; 3.1 The Linearity Properties; Exercises; 3.1.1 |
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Computer Projects; Exercises; 3.2 Matrix Multiplication (Composition); Partitioned Matrices; Computational Issues: Parallel Computing; Exercises; 3.2.1 Computer Projects; Exercises; 3.2.2 Applications to Graph Theory II; Self-Study Questions; Exercises |
3.3 Inverses Computational Issues: Reduction versus Inverses; Exercises; 3.3.1 Computer Projects; Exercises; 3.3.2 Applications to Economics; Self-Study Questions; Exercises; 3.4 The LU Factorization; Exercises; 3.4.1 Computer Projects; Exercises; 3.5 The Matrix of a Linear Transformation; Coordinates; Application to Differential Equations; Isomorphism; Invertible Linear Transformations; Exercises; Computer Projects; Exercises; Chapter Summary; Chapter 4 Determinants; 4.1 Definition of the Determinant; 4.1.1 The Rest of the Proofs; Exercises; 4.1.2 Computer Projects |
4.2 Reduction and Determinants Uniqueness of the Determinant; Exercises; 4.2.1 Volume; Exercises; A Formula for Inverses; Exercises; Chapter Summary; Chapter 5 Eigenvectors and Eigenvalues; 5.1 Eigenvectors; Exercises; 5.1.1 Computer Projects; Exercises; 5.1.2 Application to Markov Processes; Exercises; 5.2 Diagonalization; Powers of Matrices; Exercises; 5.2.1 Computer Projects; Exercises; 5.2.2 Application to Systems of Differential Equations; Exercises; 5.3 Complex Eigenvectors; Complex Vector Spaces; Exercises; 5.3.1 Computer Projects; 5.3 Exercises; Chapter Summary |
Chapter 6 Orthogonality |
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