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• Week 1:Introduction to Vectors: Vectors and Linear Combinations, Lengths and Dot Products, Matrices.
• Week 2:Solving Linear Equations: Vectors and Linear Equations, the Idea of Elimination, Elimination Using Matrices..
• Week 3:Rules for Matrix Operations, Inverse Matrices
• Week 4: Elimination = Factorization; A = LU, Transposes and Permutations
• Week 5: Vector Spaces and Subspaces: Spaces of Vectors, The Null space of A: Solving Ax = 0, The Rank and the Row Reduced Form, the Complete Solution to Ax = B
• Week 6:Independence, Basis and Dimension, Dimensions of the Four Subspaces.
• Week 7:Orthogonally: Orthogonally of the Four Subspaces, Projections.
• Week 8: least squares approximations ,Orthogonal Bases and Gram-Schmidt.
• Week 9: mid term exam
• Week 10: Determinants: The Properties of Determinants, Permutations and Cofactors, Cramer's Rule, Inverses, and Volumes.
• Week 11: Eigenvalues and Eigenvectors: Introduction to Eigenvalues, Diagonalizing a Matrix, Applications to Differential Equations
• Week 12:Symmetric Matrices, Positive Definite Matrices, Similar Matrices, Singular Value Decomposition (SVD).
• Week 13: Applications: Matrices in Engineering, Graphs and Networks, Markov MatricesPopulation, and Economics; Linear Programming.
• Week 14: Fourier series: Linear Algebra for functions
• Week 15:Linear Algebra for Statistics and Probability, Computer Graphics.
• Week 16:Numerical Linear Algebra: Gaussian Elimination in Practice, Norms and Condition Numbers, Iterative Methods for Linear Algebra.
• Week 17:Complex Vectors and Matrices: Complex Numbers, Hermitian and Unitary Matrices, Matrix Factorizations.
• Week 18: Final Exam