Exploring Linear Algebra: Labs and Projects with Mathematica ®

Content: Matrix Operations  Lab 0: An Introduction to Mathematica  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 x 4 Determinants and Beyond  Project Set 1       Invertibility  Lab 7: Singular or Nonsingular? Why Singularity Matters  Lab 8: Mod It Out, Matrices with Entries in Zp Lab 9: It's a Complex World  Lab 10: Declaring Independence: Is It Linear?  Project Set 2       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       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       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       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       Mathematica Demonstrations and References    Index