Suitable for advanced undergraduates and graduate students, this text offers a complete introduction to the basic concepts of linear algebra. Interesting and. A Course in Linear Algebra. Front Cover. David B. Damiano, John B. Little. Harcourt Brace Jovanvich, Jan 1, – Mathematics – pages. “Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter contains an introduction.

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A Course in Linear Algebra

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Author Damiano, David B. Other Authors Little, John B. Physical Description xvii, p. Summary “Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter contains an introduction, definitions, and propositions, iin addition to multiple examples, lemmas, theorems, corollaries, and proofs.


Each chapter features numerous supplemental exercises, and solutions to selected problems appear at the end.

Linear Dependence and Linear Independence 1. Interlude kinear Solving Systems of Linear Equations 1. Linear Transformations between Finite-Dimensional Spaces 2. Kernel and Image 2. Applications of the Dimension Theorem 2. Composition of Linear Transformations 2. The Inverse of a Linear Transformation 2. Change of Basis 3. The Determinant as Area 3. The Determinant of an n x n Matrix 3.

Further Properties of the Determinant 4. Eigenvalues and Eigenvectors 4. Geometry in R” 4. Orthogonal Projections and the Gram-Schmidt Process 4. Symmetric Matrices Contents note continued: The Spectral Theorem 5. Vector Spaces Over a Field 5. Geometry in a Complex Vector Space 6. A Canonical Form for Nilpotent Mappings 6.

Jordan Canonical Form 6. Computing Jordan Form 6. The Characteristic Polynomial and the Minimal Polynomial 7. Two Motivating Examples 7. Constant Coefficient Linear Differential Equations: The Diagonalizable Case 7. The General Case 7. An Eigenvalue Problem A1. Statements and Logical Operators A1.

Statements with Quantifiers A1. Further Notions from Set Theory Contents note continued: Relations and Functions A1. Injectivity, Surjectivity, and Bijectivity A1. Composites and Inverse Mappings A1. Some Optional Remarks on Mathematics and Logic.


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