Course Details
Contents
Introduction to vectors, elementary operations on vectors, Dot product, Norm of a vector, Caucy-Schwarz inequality, Projection, Vector Space, Subspace, Linear Combination, Span, Linear independence, Spanning Set, Basis, Orthogonal basis, representation of a vector in orthogonal basis, Graham Schmidt Algorithm, projection of a vector onto subspace, K-means Clustering, Introduction to Matrices, Matrix-Vector Product, Linear Transformations, Inverse of a Matrix, Matrix Multiplication, Fundamental Subspaces of Matrix, System of Linear Equations, Rank-Nullity Theorem, Gaussian Elimination, LU decomposition, Overdetermined System of Linear Equations, Linear Regression, Trace of a matrix, Determinant of a matrix, Eigen Values and Eigen Vectors, Spectral Theorem, Rayleigh quotient, Quadratic Forms, Positive Definite matrices, Positive semidefinite matrices, Cholesky decomposition, QR decomposition, Singular value decomposition (SVD), Matrix Norms and Principal component Analysis.
References
1. Gilbert Strang, “Linear Algebra and its applications”, Cengage Learning
2. S H FriedBerg, A J Insel, L E Spence, “Linear Algebra”, PHI Learning
3. S Boyd and L Vandenberghe, “Introduction to Applied Linear Algebra”, Cambridge university press [ebook available on Prof. Boyd’s Webpage]
4. E Kreyszig, “Advanced Engineering Mathematics”, Wiley.
5. M Greenberg, “Advanced Engineering Mathematics”, Pearson