A Modern Introduction to Linear Algebra
CRC Press, 21. okt. 2009 - 670 sider
Useful Concepts and Results at the Heart of Linear Algebra
A Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. Concrete, easy-to-understand examples motivate the theory.
The book first discusses vectors, Gaussian elimination, and reduced row echelon forms. It then offers a thorough introduction to matrix algebra, including defining the determinant naturally from the PA=LU factorization of a matrix. The author goes on to cover finite-dimensional real vector spaces, infinite-dimensional spaces, linear transformations, and complex vector spaces. The final chapter presents Hermitian and normal matrices as well as quadratic forms.
Taking a computational, algebraic, and geometric approach to the subject, this book provides the foundation for later courses in higher mathematics. It also shows how linear algebra can be used in various areas of application. Although written in a "pencil and paper" manner, the text offers ample opportunities to enhance learning with calculators or computer usage.
Solutions manual available for qualifying instructors
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Chapter 2 Systems of Equations
Chapter 3 Matrix Algebra
Chapter 4 Eigenvalues Eigenvectors and Diagonalization
Chapter 5 Vector Spaces
Chapter 6 Linear Transformations
Chapter 7 Inner Product Spaces
Chapter 8 Hermitian Matrices and Quadratic Forms