Exploring linear algebra : labs and projects with MATLAB® Cover Half Title Series Page Title Page Copyright Page Contents Preface Acknowledgments 1 Matrix Operations Lab 0: An Introduction to MATLAB® Lab 1: Matrix Basics and Operations Lab 2: A Matrix Representation of Linear Systems Lab 3: Powers Inverses and Special Matrices Lab 4: Graph Theory and Adjacency Matrices Lab 5: Permutations and Determinants Lab 6: 4 × 4 Determinants and Beyond Project Set 1 2 Invertibility Lab 7: Singular or Nonsingular Why Singularity Matters Lab 8: Mod It Out Matrices with Entries in Zp Lab 9: Its a Complex World Lab 10: Declaring Independence: Is It Linear Project Set 2 3 Vector Spaces Lab 11: Vector Spaces and Subspaces Lab 12: Basing It All on Just a Few Vectors Lab 13: Linear Transformations Lab 14: Eigenvalues and Eigenspaces Lab 15: Markov Chains: An Application of Eigenvalues Project Set 3 4 Orthogonality Lab 16: Inner Product Spaces Lab 17: The Geometry of Vector and Inner Product Spaces Lab 18: Orthogonal Matrices QR Decomposition and Least Squares Regression Lab 19: Symmetric Matrices and Quadratic Forms Project Set 4 5 Matrix Decomposition with Applications Lab 20: Singular Value Decomposition (SVD) Lab 21: Cholesky Decomposition and Its Application to Statistics Lab 22: Jordan Canonical Form Project Set 5 6 Applications to Differential Equations Lab 23: Linear Differential Equations Lab 24: Higher Order Linear Differential Equations Lab 25: Phase Portraits Using the Jacobian Matrix to Look Closer at Equilibria Project Set 6 MATLAB Demonstrations and References Index.