Linear Algebra Tools for Data Mining:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2012
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | MATLAB Computations Preface; Contents; Part 1 Linear Algebra; 1. Modules and Linear Spaces; 1.1 Introduction; 1.2 Permutations; 1.3 Groups, Rings, and Fields; 1.4 Closure and Interior Systems; 1.5 Modules; 1.6 Linear Mappings; 1.7 Submodules; 1.8 Linear Combinations; 1.9 The Lattice of Submodules of a Module; 1.10 Linear Independence; 1.11 Linear Spaces; 1.12 Module Isomorphism Theorems; 1.13 Direct Sums and Direct Products; 1.14 Dual Modules and Linear Spaces; 1.15 Topological Linear Spaces; Exercises and Supplements; Bibliographical Comments; 2. Matrices; 2.1 Introduction; 2.2 Matrices with Arbitrary Elements 2.3 Rings and Matrices2.4 Special Classes of Matrices; 2.5 Complex Matrices; 2.6 Partitioned Matrices and Matrix Operations; 2.7 Invertible Matrices; 2.8 Matrices and Linear Transformations; 2.9 The Notion of Rank; 2.10 Matrix Similarity and Congruence; 2.11 Linear Systems and Matrices; 2.12 The Row Echelon Form of Matrices; 2.13 The Kronecker and Hadamard Products; 2.14 Linear Inequalities; 2.15 Complex Multilinear Forms; Exercises and Supplements; Bibliographical Comments; 3. MATLAB; 3.1 Introduction; 3.2 The Interactive Environment of MATLAB. 3.3 Number Representation and Arithmetic Computations3.4 Matrices Representation; 3.5 Random Matrices; 3.6 Control Structures; 3.7 Indexing; 3.8 Functions; 3.9 Matrix Computations; Exercises and Supplements; Bibliographical Comments; 4. Determinants; 4.1 Introduction; 4.2 Multilinear Forms; 4.3 Cramer's Formula; 4.4 Partitioned Matrices and Determinants; MATLAB Computations; Exercises and Supplements; Bibliographical Comments; 5. Norms on Linear Spaces; 5.1 Introduction; 5.2 Fundamental Inequalities; 5.3 Metric Spaces; 5.4 Norms; 5.5 Vector Norms on Rn 5.6 The Topology of Normed Linear Spaces5.7 Norms for Matrices; 5.8 Matrix Sequences and Matrix Series; 5.9 Condition Numbers for Matrices; 5.10 Conjugate Norms; MATLAB Computations; Exercises and Supplements; Bibliographical Comments; 6. Inner Product Spaces; 6.1 Introduction; 6.2 Inner Products and Norms; 6.3 Orthogonality; 6.4 Hyperplanes in Rn; 6.5 Unitary and Orthogonal Matrices; 6.6 Projection on Subspaces; 6.7 Positive Definite and Positive Semidefinite Matrices; 6.8 The Gram-Schmidt Orthogonalization Algorithm; 6.9 The QR Factorization of Matrices; 6.10 Matrix Groups MATLAB ComputationsExercises and Supplements; Bibliographical Comments; 7. Convexity; 7.1 Introduction; 7.2 Convex Sets; 7.3 Separation of Convex Sets; 7.4 Cones in Rn; 7.5 Convex Functions; 7.6 Convexity and Inequalities; 7.7 Constrained Extrema and Convexity; Exercises and Supplements; Bibliographical Comments; 8. Eigenvalues; 8.1 Introduction; 8.2 Eigenvalues and Eigenvectors; 8.3 The Characteristic Polynomial of a Matrix; 8.4 Spectra of Special Matrices; 8.5 Geometry of Eigenvalues; 8.6 Spectra of Kronecker Products; 8.7 The Power Method for Eigenvalues; 8.8 The QR Iterative Algorithm This comprehensive volume presents the foundations of linear algebra ideas and techniques applied to data mining and related fields. Linear algebra has gained increasing importance in data mining and pattern recognition, as shown by the many current data mining publications, and has a strong impact in other disciplines like psychology, chemistry, and biology. The basic material is accompanied by more than 550 exercises and supplements, many accompanied with complete solutions and MATLAB applications Includes bibliographical references and index |
| Beschreibung: | 1 Online-Ressource (878 pages) |
| ISBN: | 9789814383509 9814383503 1280669896 9781280669897 9789814383493 981438349X |
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| 500 | |a MATLAB Computations | ||
| 500 | |a Preface; Contents; Part 1 Linear Algebra; 1. Modules and Linear Spaces; 1.1 Introduction; 1.2 Permutations; 1.3 Groups, Rings, and Fields; 1.4 Closure and Interior Systems; 1.5 Modules; 1.6 Linear Mappings; 1.7 Submodules; 1.8 Linear Combinations; 1.9 The Lattice of Submodules of a Module; 1.10 Linear Independence; 1.11 Linear Spaces; 1.12 Module Isomorphism Theorems; 1.13 Direct Sums and Direct Products; 1.14 Dual Modules and Linear Spaces; 1.15 Topological Linear Spaces; Exercises and Supplements; Bibliographical Comments; 2. Matrices; 2.1 Introduction; 2.2 Matrices with Arbitrary Elements | ||
| 500 | |a 2.3 Rings and Matrices2.4 Special Classes of Matrices; 2.5 Complex Matrices; 2.6 Partitioned Matrices and Matrix Operations; 2.7 Invertible Matrices; 2.8 Matrices and Linear Transformations; 2.9 The Notion of Rank; 2.10 Matrix Similarity and Congruence; 2.11 Linear Systems and Matrices; 2.12 The Row Echelon Form of Matrices; 2.13 The Kronecker and Hadamard Products; 2.14 Linear Inequalities; 2.15 Complex Multilinear Forms; Exercises and Supplements; Bibliographical Comments; 3. MATLAB; 3.1 Introduction; 3.2 The Interactive Environment of MATLAB. | ||
| 500 | |a 3.3 Number Representation and Arithmetic Computations3.4 Matrices Representation; 3.5 Random Matrices; 3.6 Control Structures; 3.7 Indexing; 3.8 Functions; 3.9 Matrix Computations; Exercises and Supplements; Bibliographical Comments; 4. Determinants; 4.1 Introduction; 4.2 Multilinear Forms; 4.3 Cramer's Formula; 4.4 Partitioned Matrices and Determinants; MATLAB Computations; Exercises and Supplements; Bibliographical Comments; 5. Norms on Linear Spaces; 5.1 Introduction; 5.2 Fundamental Inequalities; 5.3 Metric Spaces; 5.4 Norms; 5.5 Vector Norms on Rn | ||
| 500 | |a 5.6 The Topology of Normed Linear Spaces5.7 Norms for Matrices; 5.8 Matrix Sequences and Matrix Series; 5.9 Condition Numbers for Matrices; 5.10 Conjugate Norms; MATLAB Computations; Exercises and Supplements; Bibliographical Comments; 6. Inner Product Spaces; 6.1 Introduction; 6.2 Inner Products and Norms; 6.3 Orthogonality; 6.4 Hyperplanes in Rn; 6.5 Unitary and Orthogonal Matrices; 6.6 Projection on Subspaces; 6.7 Positive Definite and Positive Semidefinite Matrices; 6.8 The Gram-Schmidt Orthogonalization Algorithm; 6.9 The QR Factorization of Matrices; 6.10 Matrix Groups | ||
| 500 | |a MATLAB ComputationsExercises and Supplements; Bibliographical Comments; 7. Convexity; 7.1 Introduction; 7.2 Convex Sets; 7.3 Separation of Convex Sets; 7.4 Cones in Rn; 7.5 Convex Functions; 7.6 Convexity and Inequalities; 7.7 Constrained Extrema and Convexity; Exercises and Supplements; Bibliographical Comments; 8. Eigenvalues; 8.1 Introduction; 8.2 Eigenvalues and Eigenvectors; 8.3 The Characteristic Polynomial of a Matrix; 8.4 Spectra of Special Matrices; 8.5 Geometry of Eigenvalues; 8.6 Spectra of Kronecker Products; 8.7 The Power Method for Eigenvalues; 8.8 The QR Iterative Algorithm | ||
| 500 | |a This comprehensive volume presents the foundations of linear algebra ideas and techniques applied to data mining and related fields. Linear algebra has gained increasing importance in data mining and pattern recognition, as shown by the many current data mining publications, and has a strong impact in other disciplines like psychology, chemistry, and biology. The basic material is accompanied by more than 550 exercises and supplements, many accompanied with complete solutions and MATLAB applications | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Computer science | |
| 650 | 7 | |a COMPUTERS / Database Management / Data Mining |2 bisacsh | |
| 650 | 7 | |a COMPUTERS / Enterprise Applications / Business Intelligence Tools |2 bisacsh | |
| 650 | 7 | |a COMPUTERS / Intelligence (AI) & Semantics |2 bisacsh | |
| 650 | 7 | |a Computer algorithms |2 fast | |
| 650 | 7 | |a Data mining |2 fast | |
| 650 | 7 | |a Linear programming |2 fast | |
| 650 | 7 | |a Parallel processing (Electronic computers) |2 fast | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Data mining | |
| 650 | 4 | |a Parallel processing (Electronic computers) | |
| 650 | 4 | |a Computer algorithms | |
| 650 | 4 | |a Linear programming | |
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Datensatz im Suchindex
| _version_ | 1804175282555322368 |
|---|---|
| any_adam_object | |
| author | Simovici, Dan A. |
| author_GND | (DE-588)128892447 |
| author_facet | Simovici, Dan A. |
| author_role | aut |
| author_sort | Simovici, Dan A. |
| author_variant | d a s da das |
| building | Verbundindex |
| bvnumber | BV042961136 |
| collection | ZDB-4-EBA ZDB-4-EBU |
| ctrlnum | (OCoLC)794328371 (DE-599)BVBBV042961136 |
| dewey-full | 006.3 006.312 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.3 006.312 |
| dewey-search | 006.3 006.312 |
| dewey-sort | 16.3 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:13:49Z |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Simovici, Dan A. Verfasser (DE-588)128892447 aut Linear Algebra Tools for Data Mining Singapore World Scientific 2012 1 Online-Ressource (878 pages) txt rdacontent c rdamedia cr rdacarrier MATLAB Computations Preface; Contents; Part 1 Linear Algebra; 1. Modules and Linear Spaces; 1.1 Introduction; 1.2 Permutations; 1.3 Groups, Rings, and Fields; 1.4 Closure and Interior Systems; 1.5 Modules; 1.6 Linear Mappings; 1.7 Submodules; 1.8 Linear Combinations; 1.9 The Lattice of Submodules of a Module; 1.10 Linear Independence; 1.11 Linear Spaces; 1.12 Module Isomorphism Theorems; 1.13 Direct Sums and Direct Products; 1.14 Dual Modules and Linear Spaces; 1.15 Topological Linear Spaces; Exercises and Supplements; Bibliographical Comments; 2. Matrices; 2.1 Introduction; 2.2 Matrices with Arbitrary Elements 2.3 Rings and Matrices2.4 Special Classes of Matrices; 2.5 Complex Matrices; 2.6 Partitioned Matrices and Matrix Operations; 2.7 Invertible Matrices; 2.8 Matrices and Linear Transformations; 2.9 The Notion of Rank; 2.10 Matrix Similarity and Congruence; 2.11 Linear Systems and Matrices; 2.12 The Row Echelon Form of Matrices; 2.13 The Kronecker and Hadamard Products; 2.14 Linear Inequalities; 2.15 Complex Multilinear Forms; Exercises and Supplements; Bibliographical Comments; 3. MATLAB; 3.1 Introduction; 3.2 The Interactive Environment of MATLAB. 3.3 Number Representation and Arithmetic Computations3.4 Matrices Representation; 3.5 Random Matrices; 3.6 Control Structures; 3.7 Indexing; 3.8 Functions; 3.9 Matrix Computations; Exercises and Supplements; Bibliographical Comments; 4. Determinants; 4.1 Introduction; 4.2 Multilinear Forms; 4.3 Cramer's Formula; 4.4 Partitioned Matrices and Determinants; MATLAB Computations; Exercises and Supplements; Bibliographical Comments; 5. Norms on Linear Spaces; 5.1 Introduction; 5.2 Fundamental Inequalities; 5.3 Metric Spaces; 5.4 Norms; 5.5 Vector Norms on Rn 5.6 The Topology of Normed Linear Spaces5.7 Norms for Matrices; 5.8 Matrix Sequences and Matrix Series; 5.9 Condition Numbers for Matrices; 5.10 Conjugate Norms; MATLAB Computations; Exercises and Supplements; Bibliographical Comments; 6. Inner Product Spaces; 6.1 Introduction; 6.2 Inner Products and Norms; 6.3 Orthogonality; 6.4 Hyperplanes in Rn; 6.5 Unitary and Orthogonal Matrices; 6.6 Projection on Subspaces; 6.7 Positive Definite and Positive Semidefinite Matrices; 6.8 The Gram-Schmidt Orthogonalization Algorithm; 6.9 The QR Factorization of Matrices; 6.10 Matrix Groups MATLAB ComputationsExercises and Supplements; Bibliographical Comments; 7. Convexity; 7.1 Introduction; 7.2 Convex Sets; 7.3 Separation of Convex Sets; 7.4 Cones in Rn; 7.5 Convex Functions; 7.6 Convexity and Inequalities; 7.7 Constrained Extrema and Convexity; Exercises and Supplements; Bibliographical Comments; 8. Eigenvalues; 8.1 Introduction; 8.2 Eigenvalues and Eigenvectors; 8.3 The Characteristic Polynomial of a Matrix; 8.4 Spectra of Special Matrices; 8.5 Geometry of Eigenvalues; 8.6 Spectra of Kronecker Products; 8.7 The Power Method for Eigenvalues; 8.8 The QR Iterative Algorithm This comprehensive volume presents the foundations of linear algebra ideas and techniques applied to data mining and related fields. Linear algebra has gained increasing importance in data mining and pattern recognition, as shown by the many current data mining publications, and has a strong impact in other disciplines like psychology, chemistry, and biology. The basic material is accompanied by more than 550 exercises and supplements, many accompanied with complete solutions and MATLAB applications Includes bibliographical references and index Algebra Computer science COMPUTERS / Database Management / Data Mining bisacsh COMPUTERS / Enterprise Applications / Business Intelligence Tools bisacsh COMPUTERS / Intelligence (AI) & Semantics bisacsh Computer algorithms fast Data mining fast Linear programming fast Parallel processing (Electronic computers) fast Informatik Data mining Parallel processing (Electronic computers) Computer algorithms Linear programming Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Data Mining (DE-588)4428654-5 gnd rswk-swf Data Mining (DE-588)4428654-5 s Lineare Algebra (DE-588)4035811-2 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457172 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Simovici, Dan A. Linear Algebra Tools for Data Mining Algebra Computer science COMPUTERS / Database Management / Data Mining bisacsh COMPUTERS / Enterprise Applications / Business Intelligence Tools bisacsh COMPUTERS / Intelligence (AI) & Semantics bisacsh Computer algorithms fast Data mining fast Linear programming fast Parallel processing (Electronic computers) fast Informatik Data mining Parallel processing (Electronic computers) Computer algorithms Linear programming Lineare Algebra (DE-588)4035811-2 gnd Data Mining (DE-588)4428654-5 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4428654-5 |
| title | Linear Algebra Tools for Data Mining |
| title_auth | Linear Algebra Tools for Data Mining |
| title_exact_search | Linear Algebra Tools for Data Mining |
| title_full | Linear Algebra Tools for Data Mining |
| title_fullStr | Linear Algebra Tools for Data Mining |
| title_full_unstemmed | Linear Algebra Tools for Data Mining |
| title_short | Linear Algebra Tools for Data Mining |
| title_sort | linear algebra tools for data mining |
| topic | Algebra Computer science COMPUTERS / Database Management / Data Mining bisacsh COMPUTERS / Enterprise Applications / Business Intelligence Tools bisacsh COMPUTERS / Intelligence (AI) & Semantics bisacsh Computer algorithms fast Data mining fast Linear programming fast Parallel processing (Electronic computers) fast Informatik Data mining Parallel processing (Electronic computers) Computer algorithms Linear programming Lineare Algebra (DE-588)4035811-2 gnd Data Mining (DE-588)4428654-5 gnd |
| topic_facet | Algebra Computer science COMPUTERS / Database Management / Data Mining COMPUTERS / Enterprise Applications / Business Intelligence Tools COMPUTERS / Intelligence (AI) & Semantics Computer algorithms Data mining Linear programming Parallel processing (Electronic computers) Informatik Lineare Algebra Data Mining |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457172 |
| work_keys_str_mv | AT simovicidana linearalgebratoolsfordatamining |