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|a 9781118800416
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|a 1118800419
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|a (OCoLC)1347025109
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|a (OCoLC)on1347025109
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|a Gruber, Marvin H. J.
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| 245 |
1 |
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|a Matrix Algebra for Linear Models
|h [electronic resource].
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| 260 |
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|a Newark :
|b John Wiley & Sons, Incorporated,
|c 2013.
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| 300 |
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|a 1 online resource (393 p.).
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| 490 |
1 |
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|a New York Academy of Sciences Ser.
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| 500 |
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|a Description based upon print version of record.
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| 500 |
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|a 10.2 Reparameterization of a Non-full-Rank Model to a Full-Rank Model
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| 505 |
0 |
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|a Intro -- Matrix Algebra for Linear Models -- Copyright -- Contents -- Preface -- Acknowledgments -- Part I Basic Ideas about Matrices and Systems of Linear Equations -- Section 1 What Matrices Are and Some Basic Operations with Them -- 1.1 Introduction -- 1.2 What Are Matrices and Why Are They Interesting to a Statistician? -- 1.3 Matrix Notation, Addition, and Multiplication -- 1.4 Summary -- Exercises -- Section 2 Determinants and Solving a System of Equations -- 2.1 Introduction -- 2.2 Definition of and Formulae for Expanding Determinants
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| 505 |
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|a 2.3 Some Computational Tricks for the Evaluation of Determinants -- 2.4 Solution to Linear Equations Using Determinants -- 2.5 Gauss Elimination -- 2.6 Summary -- Exercises -- Section 3 The Inverse of a Matrix -- 3.1 Introduction -- 3.2 The Adjoint Method of Finding the Inverse of a Matrix -- 3.3 Using Elementary Row Operations -- 3.4 Using the Matrix Inverse to Solve a System of Equations -- 3.5 Partitioned Matrices and Their Inverses -- 3.6 Finding the Least Square Estimator -- 3.7 Summary -- Exercises -- Section 4 Special Matrices and Facts about Matrices That Will Be Used in the Sequel
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| 505 |
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|a 4.1 Introduction -- 4.2 Matrices of the Form aIn+bJ n -- 4.3 Orthogonal Matrices -- 4.4 Direct Product of Matrices -- 4.5 An Important Property of Determinants -- 4.6 The Trace of a Matrix -- 4.7 Matrix Differentiation -- 4.8 The Least Square Estimator Again -- 4.9 Summary -- Exercises -- Section 5 Vector Spaces -- 5.1 Introduction -- 5.2 What Is a Vector Space? -- 5.3 The Dimension of a Vector Space -- 5.4 Inner Product Spaces -- 5.5 Linear Transformations -- 5.6 Summary -- Exercises -- Section 6 The Rank of a Matrix and Solutions to Systems of Equations -- 6.1 Introduction
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| 505 |
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|a 6.2 The Rank of a Matrix -- 6.3 Solving Systems of Equations with Coefficient Matrix of Less than Full Rank -- 6.4 Summary -- Exercises -- Part II Eigenvalues, the Singular Value Decomposition, and Principal Components -- Section 7 Finding the Eigenvalues of a Matrix -- 7.1 Introduction -- 7.2 Eigenvalues and Eigenvectors of a Matrix -- 7.3 Nonnegative Definite Matrices -- 7.4 Summary -- Exercises -- Section 8 The Eigenvalues and Eigenvectors of Special Matrices -- 8.1 Introduction -- 8.2 Orthogonal, Nonsingular, and Idempotent Matrices -- 8.3 The Cayley-Hamilton Theorem
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| 505 |
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|a 8.4 The Relationship between the Trace, the Determinant, and the Eigenvalues of a Matrix -- 8.5 The Eigenvalues and Eigenvectors of the Kronecker Product of Two Matrices -- 8.6 The Eigenvalues and the Eigenvectors of a Matrix of the Form aI + bJ -- 8.7 The Loewner Ordering -- 8.8 Summary -- Exercises -- Section 9 The Singular Value Decomposition (SVD) -- 9.1 Introduction -- 9.2 The Existence of the SVD -- 9.3 Uses and Examples of the SVD -- 9.4 Summary -- Exercises -- Section 10 Applications of the Singular Value Decomposition -- 10.1 Introduction
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| 590 |
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|a ProQuest Ebook Central
|b Ebook Central Academic Complete
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|a Electronic books.
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|a Matrix algebra for linear models (Text)
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|i Print version:
|a Gruber, Marvin H. J.
|t Matrix Algebra for Linear Models
|d Newark : John Wiley & Sons, Incorporated,c2013
|z 9781118592557
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