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