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Textbooks of Matrices

Hari Kishan

Edit� par Atlantic Pub, 2023

ISBN 10 : 8126910003 ISBN 13 : 9788126910007

Neuf Couverture rigide

Vendeur : Vedams eBooks (P) Ltd, New Delhi, Inde

�valuation du vendeur 4 sur 5 �toiles

Hardcover. Etat : New. Contents Preface. 1. Definitions addition and multiplication. 2. Special matrices. 3. Determinants. 4. Adjoint and inverse of a Matrix. 5. Rank. 6. Linear equations. 7. Linear independence and dependence of vectors. 8. Characteristic roots and vectors Cayley Hamilton Theorem. 9. Quadratic Forms. A Matrix is an ordered set of numbers listed in rectangular form having certain rows and columns. The knowledge of matrices is considered necessary in various areas of mathematics and a wide variety of other subjects like chemistry sociology genetics and electrical engineering. The importance of Matrix Theory has greatly increased with the invention of electronic Bain Computer. It has become a powerful tool of modern mathematics and is now extensively used in the allied fields of mathematics including probability statistics quantum mechanics mechanics etc. A Textbooks of Matrices covers all the important topics on matrices. The subject matter has been divided into nine chapters. Chapter 1 explains multiplication and addition by scalar commutative and associative matrices. Special kinds of matrices like Symmetric Skew Symmetric Hermitian Skew Hermitian Involuntary Orthogonal and Unitary have been dealt with in chapter 2. Determinants of matrices have been taken up in chapter 3 which also explains various types of permutations and inversions Sarrus's rule cofactor of an element and properties and working rules of determinants. Chapter 4 takes up adjoint and inverse of a matrix and explains elementary operations and symbols. The rank of a matrix invariance of rank through elementary transformations and reduction to normal form have been dealt with in chapter 5. Since matrices are widely used to understand different forms and systems of linear equations chapter 6 has been devoted to the study of linear equations in relation to matrices. Chapter 7 deals with linear independence and dependence of vectors and explains the difference in vectors. Characteristics roots and vectors in Cayley Hamilton Theorem have been analyzed in chapter 8. Since quadratic forms are one of the three most frequently encountered homogenous forms chapter 9 explains quadratic form as a matrix product linear transformations and reduction of quadratic forms into sum of square forms. The book is an ideal textbook on matrices. The language is simple and approach thoroughly illustrative. Several examples and theorems have been included for complete understanding of various concepts. A number of exercises have been added to provide sufficient practice to the students. It will prove immensely useful to the students and teachers of matrices. 554 pp. N� de r�f. du vendeur 72860

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