A Textbook of Matrix Algebra Jayesh M. Dhodiya

A Textbook of Matrix Algebra

Author: Jayesh M. Dhodiya
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Book Title
A Textbook of Matrix Algebra
Author
Jayesh M. Dhodiya
ISBN
9781922617385
In order to provide a balanced and comprehensive account of matrix algebra, this book covers the core theory and methods in matrix analysis. The book consists of eight chapters. Chapter 1 is an introduction to matrices that introduces matrices using real-world examples, basic definitions and operations of matrix algebra. This chapter also includes solutions of the algebraic system of equations by matrix theory. Chapter 2 introduces the rank theory and its applications. This chapter includes the solution of simultaneous non-Homogeneous and homogeneous equations and methods to identify linear dependence and linear independence of vectors. Chapter 3 introduces eigenvalues and eigenvectors with their properties and importance. This chapter also includes Cayley Hamilton Theorem and its applications. Chapter 4 discusses special operations on matrices. The chapter also includes diagonalization-powers of a square matrix, orthogonalization of a symmetric matrix and Sylvester Theorem. Chapter 5 deals with the quadratic forms of matrices. This chapter presents canonical form, Lagrange's method of reduction of a quadratic form to the diagonal form and reduction to canonical form by orthogonal transformation. Chapter 6 introduces different kinds of real and complex matrices and their properties. Chapter 7 and chapter 8 introduce different methods to solve the linear system of equations and their limitations. Chapter 7 discusses Cramer's rule (methods of determinant), method of matrix inversion, Gauss elimination Method, Gauss Jordan Method, Cholesky's triangularization method, triangularization of a symmetric matrix, LU decomposition method/Crout's method, whereas chapter 8 deals with the numerical solution of the linear system of equations. These chapters include the iterative method (Jacobi method), the Gauss- Seidel method and successive over relaxation method (SOR).For more details, please visit https: //centralwestpublishing.comBinding Type: PaperbackAuthor: Jayesh M. Dhodiya, Anita TailorPublisher: Central West PublishingPublished: 05/31/2023ISBN: 9781922617385Pages: 480Weight: 1.40lbsSize: 9.00h x 6.00w x 0.97d

In order to provide a balanced and comprehensive account of matrix algebra, this book covers the core theory and methods in matrix analysis. The book consists of eight chapters. Chapter 1 is an introduction to matrices that introduces matrices using real-world examples, basic definitions and operations of matrix algebra. This chapter also includes solutions of the algebraic system of equations by matrix theory. Chapter 2 introduces the rank theory and its applications. This chapter includes the solution of simultaneous non-Homogeneous and homogeneous equations and methods to identify linear dependence and linear independence of vectors. Chapter 3 introduces eigenvalues and eigenvectors with their properties and importance. This chapter also includes Cayley Hamilton Theorem and its applications. Chapter 4 discusses special operations on matrices. The chapter also includes diagonalization-powers of a square matrix, orthogonalization of a symmetric matrix and Sylvester Theorem. Chapter 5 deals with the quadratic forms of matrices. This chapter presents canonical form, Lagrange's method of reduction of a quadratic form to the diagonal form and reduction to canonical form by orthogonal transformation. Chapter 6 introduces different kinds of real and complex matrices and their properties. Chapter 7 and chapter 8 introduce different methods to solve the linear system of equations and their limitations. Chapter 7 discusses Cramer's rule (methods of determinant), method of matrix inversion, Gauss elimination Method, Gauss Jordan Method, Cholesky's triangularization method, triangularization of a symmetric matrix, LU decomposition method/Crout's method, whereas chapter 8 deals with the numerical solution of the linear system of equations. These chapters include the iterative method (Jacobi method), the Gauss- Seidel method and successive over relaxation method (SOR).


For more details, please visit https: //centralwestpublishing.com

Binding Type: Paperback
Author: Jayesh M. Dhodiya, Anita Tailor
Publisher: Central West Publishing
Published: 05/31/2023
ISBN: 9781922617385
Pages: 480
Weight: 1.40lbs
Size: 9.00h x 6.00w x 0.97d

In order to provide a balanced and comprehensive account of matrix algebra, this book covers the core theory and methods in matrix analysis. The book consists of eight chapters. Chapter 1 is an introduction to matrices that introduces matrices using real-world examples, basic definitions and operations of matrix algebra. This chapter also includes solutions of the algebraic system of equations by matrix theory. Chapter 2 introduces the rank theory and its applications. This chapter includes the solution of simultaneous non-Homogeneous and homogeneous equations and methods to identify linear dependence and linear independence of vectors. Chapter 3 introduces eigenvalues and eigenvectors with their properties and importance. This chapter also includes Cayley Hamilton Theorem and its applications. Chapter 4 discusses special operations on matrices. The chapter also includes diagonalization-powers of a square matrix, orthogonalization of a symmetric matrix and Sylvester Theorem. Chapter 5 deals with the quadratic forms of matrices. This chapter presents canonical form, Lagrange's method of reduction of a quadratic form to the diagonal form and reduction to canonical form by orthogonal transformation. Chapter 6 introduces different kinds of real and complex matrices and their properties. Chapter 7 and chapter 8 introduce different methods to solve the linear system of equations and their limitations. Chapter 7 discusses Cramer's rule (methods of determinant), method of matrix inversion, Gauss elimination Method, Gauss Jordan Method, Cholesky's triangularization method, triangularization of a symmetric matrix, LU decomposition method/Crout's method, whereas chapter 8 deals with the numerical solution of the linear system of equations. These chapters include the iterative method (Jacobi method), the Gauss- Seidel method and successive over relaxation method (SOR).


For more details, please visit https: //centralwestpublishing.com

Binding Type: Paperback
Author: Jayesh M. Dhodiya, Anita Tailor
Publisher: Central West Publishing
Published: 05/31/2023
ISBN: 9781922617385
Pages: 480
Weight: 1.40lbs
Size: 9.00h x 6.00w x 0.97d