Course

Syllabus

Module 1: Vectors, Matrices, and Wireless Data Modeling Vectors, linear combinations, dot products, norms,Matrix operations, vector spaces, subspaces, linear independence, Rank, null space, column space

Module 2: Linear Systems and Matrix Factorizations 

Solving systems: Gaussian elimination, LU decomposition, Matrix inversion and conditioning, Introduction to overfitting and ill-posed systems in ML 

Module 3: Orthogonality and Dimensionality Reduction, Inner products, orthogonal projections, Gram-Schmidt orthogonalization, SVD and PCA, Covariance matrices and eigen decomposition 

Practical Tasks: Perform PCA on wireless sensor data to reduce feature space, Visualize and compress signal/image data using SVD 

Module 4: Linear Transformations and Learning Representations 

Kernel and image of linear transformations, Change of basis, similarity, diagonalization, Introduction to kernels in ML (basis transformation idea) 

Module 5: Least Squares, Eigenvalues, and Iterative Solutions 

Least squares approximation, Eigenvalues/eigenvectors in system analysis, Iterative methods (Jacobi, Gauss-Seidel, gradient descent preview) 

Practical Tasks: 

• Implement least squares regression and compare with gradient descent
• Use eigenvalues to perform spectral clustering on simulated network traffic

Course Outcome Statement (CO) 

CO – PO Affinity Map 

3-strong, 2-moderate, 1-weak 

1. Golub and Loan, “Matrix Computations”, Third Edition, John Hopkins University Press, 1996.  
2. Carl. D. Meyer, “Matrix Analysis and Applied Liner Algebra”, SIAM, 2001.  
3. Gilbert Strang, “Introduction to Linear Algebra”, Fourth Edition, Wellesley Cambridge Press, 2009.