![]() Linear Algebra and Its Applications David C. INTRODUCTORY EXAMPLE: The Platonic Solids.Ī: Uniqueness of the Reduced Echelon Form.Īnswers to Odd-Numbered Exercises. INTRODUCTORY EXAMPLE: Multichannel Image Processing.ħ.1 Diagonalization of Symmetric Matrices.ħ.3 Constrained Optimization.ħ.4 The Singular Value Decomposition.ħ.5 Applications to Image Processing and Statistics. ![]() INTRODUCTORY EXAMPLE: The North American Datum and GPS Navigation.Ħ.1 Inner Product, Length, and Orthogonality.Ħ.4 The Gram–Schmidt Process.Ħ.6 Applications to Linear Models.Ħ.8 Applications of Inner Product Spaces. INTRODUCTORY EXAMPLE: Dynamical Systems and Spotted Owls.ĥ.1 Eigenvectors and Eigenvalues.ĥ.2 The Characteristic Equation.ĥ.4 Eigenvectors and Linear Transformations.ĥ.6 Discrete Dynamical Systems.ĥ.7 Applications to Differential Equations.ĥ.8 Iterative Estimates for Eigenvalues. INTRODUCTORY EXAMPLE: Space Flight and Control Systems.Ĥ.1 Vector Spaces and Subspaces.Ĥ.2 Null Spaces, Column Spaces, and Linear Transformations.Ĥ.3 Linearly Independent Sets Bases.Ĥ.5 The Dimension of a Vector Space.Ĥ.8 Applications to Difference Equations.Ĥ.9 Applications to Markov Chains. INTRODUCTORY EXAMPLE: Random Paths and Distortion.ģ.1 Introduction to Determinants.ģ.2 Properties of Determinants.ģ.3 Cramer’s Rule, Volume, and Linear Transformations. INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design.Ģ.2 The Inverse of a Matrix.Ģ.3 Characterizations of Invertible Matrices.Ģ.6 The Leontief Input–Output Model.Ģ.7 Applications to Computer Graphics. INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering.ġ.1 Systems of Linear Equations.ġ.2 Row Reduction and Echelon Forms.ġ.4 The Matrix Equation Ax (omited) b.ġ.5 Solution Sets of Linear Systems.ġ.6 Applications of Linear Systems.ġ.8 Introduction to Linear Transformations.ġ.9 The Matrix of a Linear Transformation.ġ.10 Linear Models in Business, Science, and Engineering.
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