Author | Jacob, Bill. author |
---|---|
Title | Linear Functions and Matrix Theory [electronic resource] / by Bill Jacob |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4218-5 |
Descript | XI, 330 p. online resource |
1 linear Functions -- 1.1 Linear Functions -- 1.2 Local Linearity -- 1.3 Matrices -- 1.4 More Linearity -- 2 Linear Geometry -- 2.1 Linear Geometry in the Plane -- 2.2 Vectors and Lines in the Plane -- 2.3 Linear Geometry in Space -- 2.4 An Introduction to Linear Perspective -- 3 Systems of Linear Equations -- 3.1 Systems of Linear Equations -- 3.2 Gaussian Elimination -- 3.3 Gauss-Jordan Elimination -- 3.4 Matrix Rank and Systems of Linear Equations -- 3.5 The Simplex Algorithm -- 4 Basic Matrix Algebra -- 4.1 The Matrix Product: A Closer Look -- 4.2 Fibonacci Numbers and Difference Equations -- 4.3 The Determinant -- 4.4 Properties and Applications of the Determinant -- 4.5 The LU-Decomposition -- 5 Key Concepts of Linear Algebra in Rn -- 5.1 Linear Combinations and Subspaces -- 5.2 Linear Independence -- 5.3 Basis and Dimension -- 6 More Vector Geometry -- 6.1 The Dot Product -- 6.2 Angles and Projections -- 6.3 The Cross Product -- 7 Eigenvalues and Eigenvectors of Matrices -- 7.1 Eigenvalues and Eigenvectors -- 7.2 Eigenspaces and Diagonalizability -- 7.3 Symmetric Matrices and Probability Matrices -- 8 Matrices as Linear Transformations -- 8.1 Linear Transformations -- 8.2 Using Linear Transformations -- 8.3 Change of Basis -- 9 Orthogonality and Least-Squares Problems -- 9.1 Orthogonality and the Gram-Schmidt Process -- 9.2 Orthogonal Projections -- 9.3 Least-Squares Approximations -- Answers to Odd-Numbered Problems