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AuthorHarville, David A. author
TitleMatrix Algebra: Exercises and Solutions [electronic resource] / by David A. Harville
ImprintNew York, NY : Springer New York : Imprint: Springer, 2001
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Descript XV, 271 p. 1 illus. online resource


This book comprises well over three-hundred exercises in matrix algebra and their solutions. The exercises are taken from my earlier book Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to make them comprehensible independently of their source. To further insure that the restated exercises have this stand-alone property, I have included in the front matter a section on terminology and another on notation. These sections provide definitions, descriptions, comments, or explanatory material pertaining to certain terms and notational symbols and conventions from Matrix Algebra From a Statistician's Perspective that may be unfamiliar to a nonreader of that book or that may differ in generality or other respects from those to which he/she is accustomed. For example, the section on terminology includes an entry for scalar and one for matrix. These are standard terms, but their use herein (and in Matrix Algebra From a Statistician's Perspective) is restricted to real numbers and to rectangular arrays of real numbers, whereas in various other presentations, a scalar may be a complex number or more generally a member of a field, and a matrix may be a rectangular array of such entities


1 Matrices -- 2 Submatrices and Partitioned Matrices -- 3 Linear Dependence and Independence -- 4 Linear Spaces: Rowand Column Spaces -- 5 Trace of a (Square) Matrix -- 6 Geometrical Considerations -- 7 Linear Systems : Consistency and Compatibility -- 8 Inverse Matrices -- 9 Generalized Inverses -- 10 Idempotent Matrices -- 11 Linear Systems: Solutions -- 12 Projections and Projection Matrices -- 13 Determinants -- 14 Linear, Bilinear, and Quadratic Forms -- 15 Matrix Differentiation -- 16 Kronecker Products and the Vec and Vech Operators -- 17 Intersections and Sums of Subspaces -- 18 Sums (and Differences) of Matrices -- 19 Minimization of a Second-Degree Polynomial (in n Variables) Subject to Linear Constraints -- 20 The Moore-Penrose Inverse -- 21 Eigenvalues and Eigenvectors -- 22 Linear Transformations -- References

Statistics Statistics Statistical Theory and Methods


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