A Modern Introduction to Linear Algebra

Forsideomslag
CRC Press, 21. okt. 2009 - 670 sider

Useful Concepts and Results at the Heart of Linear Algebra
A one- or two-semester course for a wide variety of students at the sophomore/junior undergraduate level

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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Indhold

Chapter 1 Vectors
1
Chapter 2 Systems of Equations
67
Chapter 3 Matrix Algebra
157
Chapter 4 Eigenvalues Eigenvectors and Diagonalization
253
Chapter 5 Vector Spaces
347
Chapter 6 Linear Transformations
389
Chapter 7 Inner Product Spaces
461
Chapter 8 Hermitian Matrices and Quadratic Forms
539
Basics of Set Theory
587
Summation and Product Notation
593
Mathematical Induction
597
Complex Numbers
601
AnswersHints to OddNumbered Problems
605
Index
645
Back cover
655
Copyright

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Om forfatteren (2009)

Henry Ricardo is a professor of mathematics at Medgar Evers College of the City University of New York, where he was presented with the 2008 Distinguished Service Award by the School of Science, Health and Technology. Dr. Ricardo was also given the 2009 Distinguished Service Award by the Metropolitan New York Section of the MAA, of which he is the Governor.

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