Advanced Linear Algebra (V-U)

• Introduction and overview (V-U)
• Systems of Linear Equations (V-U)
• Row Reduction and Echelon Forms (V-U)
• Null Spaces, Column Spaces, and Linear Transformations (V-U)
• Linearly Independent Sets; Bases (V-U)
• Dimension of a Vector (V-U)
• Matrix rank (V-U)
• Solution of Linear System of Equations (Jacobi Method) (V-U)
• Solution of Linear System of Equations (Gauss–Seidel Iteration Method) (V-U)
• Solution of Linear System of Equations (Relaxation Method) (V-U)
• Eigenvalues and Eigenvectors (V-U)
• The Characteristic Equation (V-U)
• Diagonalization (V-U)
• Inner Product (V-U)
• Orthogonal and Orthonormal set (V-U)
• Orthogonal Decomposition (V-U)
• Orthogonal basis, Gram-Schmidt Process, Orthonormal basis (V-U)
• Least Square Solutions (V-U)
• Eigen Value Problems (Power Method) (V-U)
• Eigen Value Problems (Jacobi’s Method) (V-U)
• Inner Product Spaces (V-U)
• Applications of inner product spaces (V-U)