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Books > Science & Mathematics > Mathematics > Algebra
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Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Paperback, 2011 ed.)
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Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Paperback, 2011 ed.)
Series: Statistics for Social and Behavioral Sciences
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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.
General
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