Basics of matrix algebra for statistics with R. (2018)

• Record Type: Book
• Further Information: Note: Nick Fieller.
• Authors: Fieller, N. R. J
• Contents: Introduction; Objectives; Further Reading; Guide to Notation; An Outline Guide to R; Inputting Data to R; Summary of Matrix Operators in R; Examples of R Commands; Vectors and Matrices; Vectors; Matrices; Matrix Arithmetic; Transpose and Trace of Sums and Products; Special Matrices; Partitioned Matrices; Algebraic Manipulation of matrices; Useful Tricks; Linear and Quadratic Forms; Creating Matrices in R; Matrix Arithmetic in R; Initial Statistical Applications Rank of Matrices; Introduction and Definitions; Rank Factorization; Rank Inequalities; Rank in Statistics; Determinants; Introduction and Definitions; Implementation in R; Properties of Determinants; Orthogonal Matrices; Determinants of Partitioned Matrices; A Key Property of Determinants; Inverses; Introduction and Definitions ; Properties; Implementation in R; Inverses of Patterned Matrices; Inverses of Partitioned Matrices; General Formulae; Initial Applications Continued; Eigenanalysis of Real Symmetric Matrices ; Introduction and Definitions; Eigenvectors; Implementation in R; Properties of Eigenanalyses; A Key Statistical Application: PCA; Matrix Exponential; Decompositions; Eigenanalysis of Matrices with Special Structures; Summary of Key Results; Vector and Matrix Calculus ; Introduction; Differentiation of a Scalar with Respect to a Vector; Differentiation of a Scalar with Respect to a Matrix; Differentiation of a Vector with Respect to a Vector; Differentiation of a Matrix with Respect to a Scalar; Use of Eigenanalysis in Constrained Optimization; Further Topics ; Introduction; Further Matrix Decompositions; Generalized Inverses; Hadamard Products ; Kronecker Products and the Vec Operator Key Applications to Statistics; Introduction; The Multivariate Normal Distribution; Principal Component Analysis; Linear Discriminant Analysis; Canonical Correlation Analysis; Classical Scaling; Linear Models Outline Solutions to Exercises Bibliography Index Exercises appear at the end of each chapter.
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2018
• Extent: 1 online resource (248 pages)
• Subjects: 519.5028553; Mathematical statistics -- Data processing; Matrices -- Data processing; R (Computer program language)
• Languages: English
• ISBNs: 9781315360058; 1315360055
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.