This text is designed for the sophomore level, first linear algebra course offered at both 2 and 4-year schools. Students taking this course are preparing for majors in math, computer science, physics, quantitative analysis, and engineering. Linear Algebra serves as a bridge between the intuitive/computational treatment usually found in freshman calculus and the more formal atmosphere of upper division courses. Most students enter linear algebra unaccustomed to working with abstracts concepts and inexperienced in communicating their thoughts in a clear and precise manner, yet their success in subsequent courses depends to a large extent on mastery of these skills. The challenge for them is to develop their mathematical sophistication while exploring the landscape of linear algebra.
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Verlagsgruppe
McGraw-Hill Education - Europe
Zielgruppe
Für höhere Schule und Studium
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ISBN-13
978-0-07-116849-6 (9780071168496)
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Schweitzer Klassifikation
Preface1 Linear Systems and Matrices1.1 - Linear Equations1.2 - Linear Systems1.3 - Matrices1.4 - Matrix Algebra1.5 - Special Matrices1.6 - Invertibility1.7 - The Transpose1.8 - Partitioned Matrices2 Euclidean n-Space2.1 - Introduction2.2 - Geometric Vectors2.3 - Euclidean n-Space2.4 - Subspaces2.5 - Spanning Sets2.6 - Linear Independence2.7 - Dimension2.8 - Rank and Nullity2.9 - Coordinates2.10- Direct Sum Depcomposition3 Orthogonality3.1 - Introduction3.2 - The Scalar Product3.3 - Orthonormal Bases3.4 - Orthogonal Projection3.5 - Orthogonal Matrices3.6 - The Cross Product3.7 - Least Squares approximation4 Linear Transformations4.1 - Introduction4.2 - Linear Transformations4.3 - Kernel and Range4.4 - Affine Subsets4.5 - Matrix Representations4.6 - Algebra of Linear Transformations4.7 - Isometries and Similarities5 The Determinant5.1 - Introduction5.2 - The Determinant Function5.3 - Properties of det(A)5.4 - The Adjoint and Cramer's Rule5.5 - Orientation and Volume6 Diagonalization6.1 - Introduction6.2 - Eigenvalues and Eigenvectors6.3 - The Characteristic Polynomial6.4 - Diagonalization of Linear Operators6.5 - Similarity and Symmetry6.6 - Quadratic Forms6.7 - Positive Definite Forms7 Abstract Vector Spaces7.1 - Introduction7.2 - Vector Spaces and Subspaces7.3 - Independence and Dimension7.4 - Linear Functions7.5 - Coordinates7.6 - Norms and Inner Products7.7 - The Space of Linear FunctionsSelected AnswersIndex
