Functional Linear Algebra

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Functional Linear Algebra is a unique text authored to address the need for a one-term linear algebra course when students have only had calculus. It does no assume students have had a proofs course. Inhaltsverzeichnis 0. Motivation. 1. Vectors. 1.1. Vector Operations. 1.2. Span. 1.3. Linear Independence. 2. Functions of Vectors. 2.1. Linear Functions. 2.2. Matrices. 2.3. Matrix Operations. 2.4. Matrix Vector Spaces. 2.5. Kernel and Range. 2.6. Row Reduction. 2.7. Applications of Row Reduction. 2.8. Solution Sets. 2.9. Large Matrix Computations. 2.10. Invertibility. 2.11. The Invertible Matrix Theorem. 3. Vector Spaces. 3.1. Basis and Coordinates. 3.2. Polynomial Vector Spaces. 3.3. Other Vector Spaces. 4. Diagonalization. 4.1. Eigenvalues and Eigenvectors. 4.2. Determinants. 4.3. Eigenspaces. 4.4. Diagonalization. 4.5. Change of Basis Matrices. 5. Computational Vector Geometry. 5.1. Length. 5.2. Orthogonality. 5.3. Orthogonal Projection. 5.4. Orthogonal Basis. A. Appendices. A.1. Complex Numbers. A.2. Mathematica. A.3. Solutions to Odd Exercises. Bibliography. Index.