Linear Algebra Tools for Data Mining.

By: Simovici, Dan AMaterial type: TextTextSeries: eBooks on DemandPublisher: Singapore : World Scientific Publishing Company, 2012Description: 1 online resource (878 p.)ISBN: 9789814383509Subject(s): Algebra | Computer algorithms | Data mining | Parallel processing (Electronic computers)Genre/Form: Electronic books.Additional physical formats: Print version:: Linear Algebra Tools for Data MiningDDC classification: 006.3 | 006.312 LOC classification: QA76.9 .D343Online resources: Click here to view this ebook.
Contents:
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
MATLAB Computations
Summary: 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.
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QA76.9 .D343 (Browse shelf) http://uttyler.eblib.com/patron/FullRecord.aspx?p=919074 Available EBL919074

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

MATLAB Computations

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.

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