http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
This text is meant to be a hands-on lab manual that can be used in class everyday to guide the exploration of the theory and applications of linear algebra. For the most part, labs can be used individually or in a sequence. Each lab consists of and explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections.The exercise sections integrate problems using Mathematica demonstrations (an online tool that can be used with an browser with java capabilities) and Matlab coding. This allows students to discover the theory and applications of linear algebra in a meaningful and memorable way
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: It's 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.
Includes bibliographical references and index.
Boca Raton : CRC Press, Taylor & Francis Group, 2019.
Textbooks in mathematics (Boca Raton, Fla.)