 # Linear Algebra

Lecture Schedule based on Lay – Linear Algebra and Its Applications 3rd Edition

 Section Lectures Topic 1.1 1 Systems of Linear Equations 1.2 1 Row Reduction and Echelon Forms 1.3 0.5 Vector Equations 1.4 1 The Matrix Equation Ax = b 1.5 1 Solution Sets of Linear Systems 1.6 0.5 Applications of Linear Systems 1.7 1 Linear Independence 1.8 0.5 Introduction to Linear Transformations 1.9 1 The Matrix of a Linear Transformation 2.1 1 Matrix Operations 2.2 1 The Inverse of a Matrix 2.3 0.5 Characterizations of Invertible Matrices 2.5 0.5 Matrix Factorizations 4.1 1 Vector Spaces and Subspaces 4.2 1 Null Spaces, Column Spaces and Linear Transformations 4.3 0.5 Linearly Independent Sets; Bases 4.5 0.5 The Dimension of a Vector Space 4.6 0.5 Rank 4.4 0.5 Coordinate Systems 4.7 1.5 Change of Basis 3.1 0.5 Introduction to Determinants 3.2 1 Properties of Determinants 3.3 0.5 Cramer’ s Rule ; Volume and Linear Transformations 5.1 1 Eigenvectors and Eigenvalues 5.2 1 The Characteristic Equation 5.3 0.5 Diagonalization 6.1 1 Inner Product , Length and Orthogonality 6.2 0.5 Orthogonal Sets 6.3 1 Orthogonal Projections 6.4 0.5 The Gram-Schmidt Process 6.5 0.5 Least- Squares Problems 7.1 1 Diagonalization of Symmetric Matrices

List of Topics for MATLAB laboratories:

1. Introduction to MATLAB
2. Systems of Linear Equations and Floating -Point Errors
3. Matrix Algebra
4. Elementary Row Operations and LU -Factorization
5. Linear Dependence, Column Space, Null Space, and Bases
6. Change of Basis and Coordinate Transformations
7. Eigenvalues and Determinants
8. Orthogonality and Least Squares

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