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Analysis of variance --- Matrix inversion --- Analyse de variance --- Matrices --- Inversion --- 519.237 --- #WWIS:IBM/STAT --- Inverse matrices --- Inverse of a matrix --- Inversion, Matrix --- Linear operators --- ANOVA (Analysis of variance) --- Variance analysis --- Mathematical statistics --- Experimental design --- Multivariate statistical methods --- Generalized inverses --- 519.237 Multivariate statistical methods --- Opérateurs linéaires --- Inverses généralisés --- Opérateurs linéaires --- Inverses généralisés

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Numerical solutions of algebraic equations --- Matrix inversion --- Matrices --- Inversion --- 512.64 --- 519.6 --- 681.3*G13 --- Inverse matrices --- Inverse of a matrix --- Inversion, Matrix --- Linear operators --- Linear and multilinear algebra. Matrix theory --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Generalized inverses --- Matrix inversion. --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 512.64 Linear and multilinear algebra. Matrix theory --- Opérateurs linéaires --- Inverses généralisés --- Opérateurs linéaires --- Inverses généralisés

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Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.

Mathematical statistics. --- Matrices. --- Multivariate analysis. --- Multivariate analysis -- Problems, exercises, etc. --- Singular value decomposition --- Matrix inversion --- Algebras, Linear --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Mathematical Statistics --- Decomposition method. --- Matrix inversion. --- Algebras, Linear. --- Linear algebra --- Inverse matrices --- Inverse of a matrix --- Inversion, Matrix --- Method, Decomposition --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Statistics. --- Statistics, general. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Linear operators --- Matrices --- Operations research --- Programming (Mathematics) --- System analysis --- Algebra, Abstract --- Generalized inverses --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Statistics .