00000cmm a22000004a 4500 UP-99796217611212392 Buklod 20241217164007.0 m go j cr cn |||aaaaa 241217s2011 it ||||go||j| ||||||engdd 9788847018396 (eBook) 8847018390 (eBook) (iLib)UPD-00215704154 CSt DMLR rda eng DMLUC QA 184.2 R6213 2011eb Robbiano, Lorenzo author Linear algebra for everyone Lorenzo Robbiano. Milano, Italy Springer-Verlag Italia c2011 1 online resource (xvii, 218 pages) illustrations text rdacontent computer rdamedia online resource rdacarrier Title Page Copyright Page Foreword Introduction Table of Contents Numerical and Symbolic Computations The equation ax = b. Let's try to solve it The equation ax = b. Be careful of mistakes The equation ax = b. Let's manipulate the symbols Exercises Part I 1 Systems of Linear Equations and Matrices 1.1 Examples of Systems of Linear Equations 1.2 Vectors and Matrices 1.3 Generic Systems of Linear Equations and Associated Matrices 1.4 The Formalism of Ax = b Exercises 2 Operations with Matrices 2.1 Sum and the product by a number 2.2 Row by column product 2.3 How much does it cost to multiply two matrices? 2.4 Some properties of the product of matrices 2.5 Inverse of a matrix Exercises 3 Solutions of Systems of Linear Equations 3.1 Elementary Matrices 3.2 Square Linear Systems, Gaussian Elimination 3.3 Effective Calculation of Matrix Inverses 3.4 How much does Gaussian Elimination cost? 3.5 The LU Decomposition 3.6 Gaussian Elimination for General Systems of Linear Equations 3.7 Determinants Exercises 4 Coordinate Systems 4.1 Scalars and Vectors 4.2 Cartesian Coordinates 4.3 The Parallelogram Rule 4.4 Orthogonal Systems, Areas, Determinants 4.5 Angles, Moduli, Scalar Products 4.6 Scalar Products and Determinants in General 4.7 Change of Coordinates 4.8 Vector Spaces and Bases Exercises Part II 5 Quadratic Forms 5.1 Equations of the Second Degree 5.2 Elementary Operations on Symmetric Matrices 5.3 Quadratic Forms, Functions, Positivity 5.4 Cholesky Decomposition Exercises 6 Orthogonality and Orthonormality 6.1 Orthonormal Tuples and Orthonormal Matrices 6.2 Rotations 6.3 Subspaces, Linear Independence, Rank, Dimension 6.4 Orthonormal Bases and the Gram-Schmidt Procedure 6.5 The QR Decomposition Exercises 7 Projections, Pseudoinverses and Least Squares 7.1 Matrices and Linear Transformations 7.2 Projections 7.3 Least Squares and Pseudoinverses Exercises 8 Endomorphisms and Diagonalization 8.1 An Example of a Plane Linear Transformation 8.2 Eigenvalues, Eigenvectors, Eigenspaces and Similarity 8.3 Powers of Matrices 8.4 The Rabbits of Fibonac 8.5 Differential Systems 8.6 Diagonalizability of Real Symmetric Matrices Exercises Part III Appendix Problems with the computer Conclusion References Index IP-based subscription, access limited to within on-campus computer network Access via Electronic Resources of the UPD University Library Website This book provides students with the rudiments of Linear Algebra, a fundamental subject for students in all areas of science and technology. The book would also be good for statistics students studying linear algebra. It is the translation of a successful textbook currently being used in Italy. The author is a mathematician sensitive to the needs of a general audience.  In addition to introducing fundamental ideas in Linear Algebra through a wide variety of interesting examples, the book also discusses topics not usually covered in an elementary text (e.g. the "cost" of operations, generalized inverses, approximate solutions).  The challenge is to show why the "everyone" in the title can find Linear Algebra useful and easy to learn. The translation has been prepared by a native English speaking mathematician, Professor Anthony V. Geramita --Provided by publisher Electronic reproduction New York SpringerLink 2011 Available via World Wide Web through SpringerLink Algebras, Linear. SpringerLink (Online service). http://link.springer.com/book/10.1007/978-88-470-1839-6 Available for University of the Philippines Diliman via SpringerLink. Click here to access FO UPD DMLR QA 184.2 R6213 2011eb Electronic Resource