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Description: The book is intended for undergraduate and graduate students of Mathematics, Engineering, Social Sciences in general. Professionals and researchers of those fields may also use it as a reference and find the book useful. It is one of the principal branches of Mathematics. The contents are arranged in such a way that a beginner can easily grasp the material step by step. The theories are made lucid through illustrated examples. No prerequisite is necessary for sequential study of the materials, except some preliminary knowledge of calculus for the Calculus part of the book. The ‘Generalized Inverse’ is essential for undergraduate and graduate study in Statistics, Numerical Analysis, Engineering, Physics and other Social Sciences of most of the institutions of the world.
Key Features :
· Most attractive feature of the book is the GRE sample tests.
· Most chapters include some definitions and ideas different from classical texts.
· Dozens of algorithms can be converted to computer programs.
· Formulation of the modal matrix in case of multiple eigenvalues in terms of grandparent, parent and daughter is perhaps a new and pleasant terminology.
· Most texts ignore the inverse of singular as well as rectangular matrices. As a result, misconception grows among learners that inverse of a matrix is only possible if it is nonsingular. This is removed at the start of the inverse matrix in sec. 8.3 mentioning 17 procedures of inversion.
· Definiteness tests occupy appropriate places in appropriate contexts such as in secs. 1.3, 3.10, 6.17, 10.11.1, 13.24.
· The submatrix and partition matrix have been dealt with in detail in chapter 4 instead of finishing the idea with definition only.
· Chapter 5 on ‘Other matrix operations’ is a special feature of the book.Reviews : "a very interesting and comprehensive text."
Professor S. Councilman, Prof. and Ex-Chairman, Department of Mathematics, California State University, Long Beach, U.S.A.,
"a major undertaking in its scope and details of exposition. I would be happy to recommend the book to our library."
Professor M. Zuhair Nashed, Department of Mathematical Science, University of Delaware, New York, DE 19716, USA
Contents: Volume1 · Chapter one- Fundamental definitions · Chapter two-Basic algebraic operations · Chapter three-Square matrix and its special forms · Chapter four-Submatrix and partition matrix · Chapter five-Other matrix operations · Chapter six-Determinants · Chapter seven-System of simultaneous linear algebraic equations · Chapter eight-Cofactor, adjoint and inverse matrices · Chapter nine-Elementary operations and matrices · Chapter ten-Rank and nullity of a matrix · Chapter eleven-Vector(linear) spaces · Chapter twelve-Linear transformation (Operators) · Chapter thirteen-Eigenvalues and Eigenvectors
Volume 2 · Chapter twelve-Linear transformation (Operators) · Chapter thirteen -Eigenvalues and eigenvectors · Chapter fourteen-Canonical forms & matrix factorization · Chapter fifteen-Bilinear and quadraic forms · Chapter sixteen-Norms and measures of matrices · Chapter seventeen-Matrix calculus · Chapter eighteen-Gneralized inversesISBN - 9788130909523
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Pages : 590
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