Linear algebra with applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, England
Pearson
[2021]
|
| Edition: | Tenth edition, global edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references |
| Physical Description: | 554 Seiten Diagramme 24 cm |
| ISBN: | 9781292354866 0321962214 |
Staff View
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| 245 | 1 | 0 | |a Linear algebra with applications |c Steven J. Leon, University of Massachusetts, Dartmouth, Lisette G. de Pillis, Harvey Mudd College |
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Record in the Search Index
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| adam_text | ntønts Preface Matrices and Systems of Equations 1.1 1.2 1.3 1.4 1.5 1.6 Systems of Linear Equations Row Echelon Form Matrix Arithmetic Matrix Algebra Elementary Matrices Partitioned Matrices MATLAB Exercises Chapter Test A—True or False Chapter Test В Determinants 2.1 2.2 2.3 The Determinant of a Matrix Properties of Determinants Additional Topics and Applications MATLAB Exercises Chapter Test A—True or False Chapter Test В Vector Spaces 3.1 3.2 3.3 3.4 3.5 3.6 Definition and Examples Subspaces Linear Independence Basis and Dimension Change of Basis Row Space and Column Space MATLAB Exercises Chapter Test A—True or False Chapter Test В 9 15 15 26 41 61 75 85 95 99 100 101 101 108 115 123 125 125 126 126 134 148 160 166 176 184 185 186 5
Linear Transformations 188 4.1 4.2 4.3 188 197 212 218 219 219 Definition and Examples Matrix Representations of Linear Transformations Similarity MATLAB Exercises Chapter Test A—True or False Chapter Test В Orthogonality 221 5.1 5.2 5.3 5.4 5.5 5.6 5.7 222 237 245 258 267 286 295 303 305 305 The Scalar Product in R Orthogonal Subspaces Least Squares Problems Inner Product Spaces Orthonormal Sets The Gram-Schmidt Orthogonalization Process Orthogonal Polynomials MATLAB Exercises Chapter Test A—True or False Chapter Test В Eigenvalues 307 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 308 323 335 353 365 382 395 403 412 416 417 Eigenvalues and Eigenvectors Systems of Linear Differential Equations Diagonalization Hermitian Matrices The Singular Value Decomposition Quadratic Forms Positive Definite Matrices Nonnegative Matrices MATLAB Exercises Chapter Test A—True or False Chapter Test В Numerical Linear Algebra 419 7.1 7.2 420 428 Floating-Point Numbers Gaussian Elimination
Contents 7.3 7.4 7.5 7.6 7.7 7.8 Pivoting Strategies Matrix Norms and Condition Numbers Orthogonal Transformations The Eigenvalue Problem Least Squares Problems Iterative Methods MATLAB Exercises Chapter Test A—True or Paise Chapter Test В 8 Canonical Forms 8.1 8.2 Nilpotent Operators The Jordan Canonical Form Appendix: MATLAB Bibliography Answers to Selected Exercises Index 7 433 439 453 464 475 487 493 498 499 501 501 512 521 533 536 549
In the wake of the computer revolution, linear algebra has grown in prominence in mathematics curricula, rivaling the significance of calculus. Linear Algebra with Applications, now in its I Oth edition, helps students negotiate this development. The text covers all topics recommended by the Linear Algebra Curriculum Study Group (LACSG) and is also concurrent with the Group’s suggestions on the use of technology in first courses in linear algebra. With extensive revisions and new exercises and applications, this book offers an enhanced opportunity to either revisit or master the fundamentals of the discipline, making it useful for lower-level and advanced courses alike. New comprehensive MATLAB computer exercises at the end of each chapter facilitate technology-assisted instruction of the subject matter, while applications added throughout the textbook illustrate the relevance of each chapter’s content. Instructors will find the content in the book easy to cover in the two-semester course format prescribed by the LACSG but also flexible enough to be taught in a one-semester course. Suggested course outlines are provided in the Preface.
|
| adam_txt |
ntønts Preface Matrices and Systems of Equations 1.1 1.2 1.3 1.4 1.5 1.6 Systems of Linear Equations Row Echelon Form Matrix Arithmetic Matrix Algebra Elementary Matrices Partitioned Matrices MATLAB Exercises Chapter Test A—True or False Chapter Test В Determinants 2.1 2.2 2.3 The Determinant of a Matrix Properties of Determinants Additional Topics and Applications MATLAB Exercises Chapter Test A—True or False Chapter Test В Vector Spaces 3.1 3.2 3.3 3.4 3.5 3.6 Definition and Examples Subspaces Linear Independence Basis and Dimension Change of Basis Row Space and Column Space MATLAB Exercises Chapter Test A—True or False Chapter Test В 9 15 15 26 41 61 75 85 95 99 100 101 101 108 115 123 125 125 126 126 134 148 160 166 176 184 185 186 5
Linear Transformations 188 4.1 4.2 4.3 188 197 212 218 219 219 Definition and Examples Matrix Representations of Linear Transformations Similarity MATLAB Exercises Chapter Test A—True or False Chapter Test В Orthogonality 221 5.1 5.2 5.3 5.4 5.5 5.6 5.7 222 237 245 258 267 286 295 303 305 305 The Scalar Product in R" Orthogonal Subspaces Least Squares Problems Inner Product Spaces Orthonormal Sets The Gram-Schmidt Orthogonalization Process Orthogonal Polynomials MATLAB Exercises Chapter Test A—True or False Chapter Test В Eigenvalues 307 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 308 323 335 353 365 382 395 403 412 416 417 Eigenvalues and Eigenvectors Systems of Linear Differential Equations Diagonalization Hermitian Matrices The Singular Value Decomposition Quadratic Forms Positive Definite Matrices Nonnegative Matrices MATLAB Exercises Chapter Test A—True or False Chapter Test В Numerical Linear Algebra 419 7.1 7.2 420 428 Floating-Point Numbers Gaussian Elimination
Contents 7.3 7.4 7.5 7.6 7.7 7.8 Pivoting Strategies Matrix Norms and Condition Numbers Orthogonal Transformations The Eigenvalue Problem Least Squares Problems Iterative Methods MATLAB Exercises Chapter Test A—True or Paise Chapter Test В 8 Canonical Forms 8.1 8.2 Nilpotent Operators The Jordan Canonical Form Appendix: MATLAB Bibliography Answers to Selected Exercises Index 7 433 439 453 464 475 487 493 498 499 501 501 512 521 533 536 549
In the wake of the computer revolution, linear algebra has grown in prominence in mathematics curricula, rivaling the significance of calculus. Linear Algebra with Applications, now in its I Oth edition, helps students negotiate this development. The text covers all topics recommended by the Linear Algebra Curriculum Study Group (LACSG) and is also concurrent with the Group’s suggestions on the use of technology in first courses in linear algebra. With extensive revisions and new exercises and applications, this book offers an enhanced opportunity to either revisit or master the fundamentals of the discipline, making it useful for lower-level and advanced courses alike. New comprehensive MATLAB computer exercises at the end of each chapter facilitate technology-assisted instruction of the subject matter, while applications added throughout the textbook illustrate the relevance of each chapter’s content. Instructors will find the content in the book easy to cover in the two-semester course format prescribed by the LACSG but also flexible enough to be taught in a one-semester course. Suggested course outlines are provided in the Preface. |
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| id | DE-604.BV047469646 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:08:40Z |
| indexdate | 2024-07-10T09:12:59Z |
| institution | BVB |
| isbn | 9781292354866 0321962214 |
| language | English |
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| physical | 554 Seiten Diagramme 24 cm |
| publishDate | 2021 |
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| spelling | Leon, Steven J. 1943- Verfasser (DE-588)140563679 aut Linear algebra with applications Steven J. Leon, University of Massachusetts, Dartmouth, Lisette G. de Pillis, Harvey Mudd College Tenth edition, global edition Harlow, England Pearson [2021] 554 Seiten Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s DE-604 Pillis, Lisette G. de Verfasser aut Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032871328&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032871328&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Leon, Steven J. 1943- Pillis, Lisette G. de Linear algebra with applications Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Linear algebra with applications |
| title_auth | Linear algebra with applications |
| title_exact_search | Linear algebra with applications |
| title_exact_search_txtP | Linear algebra with applications |
| title_full | Linear algebra with applications Steven J. Leon, University of Massachusetts, Dartmouth, Lisette G. de Pillis, Harvey Mudd College |
| title_fullStr | Linear algebra with applications Steven J. Leon, University of Massachusetts, Dartmouth, Lisette G. de Pillis, Harvey Mudd College |
| title_full_unstemmed | Linear algebra with applications Steven J. Leon, University of Massachusetts, Dartmouth, Lisette G. de Pillis, Harvey Mudd College |
| title_short | Linear algebra with applications |
| title_sort | linear algebra with applications |
| topic | Algebras, Linear Textbooks Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Algebras, Linear Textbooks Lineare Algebra |
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