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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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