Title : Applied Linear Algebra
Course No : EE5120
Credits :
Prerequisite :

Syllabus :

Linear System of Equations: Gaussian Elimination, Echelon forms, Existence/Uniqueness/Multiplicity of solution
Vector Spaces: Definition, Subspaces, linear dependence, spanning sets, Basis, dimension, Four fundamental subspaces associated with a matrix, revisit the system of linear equations, Intersection and Sum of Subspaces, Direct Sums, Embedding of sub- spaces

Linear Transformations: Definition, Matrix representations, Change of Basis, Similarity transformations, Invertible transformations

Inner Products: Definition, induced norm, inequalities, Orthogonality, Gram-Schmidt orthogonalization process, Orthogonal projections, rank-one projections, Unitary transformations, isometry

Eigen Decomposition: Eigen vectors, Eigen Values, Gershgorin circles, Characteristic polynomial, Eigen spaces, Diagonalizability conditions, Invariant subspaces, Spectral theorem, Rayleigh quotient

Text Books :

G. Strang, “Linear Algebra and its applications”, 3rd Edition

C.D.Meyer,”Matrix analysis and applied linear algebra”, SIAM, 2000

References :

  1. D. C. Lay, “Linear algebra and its applications”, Pearson, 3rd edition
  2. S. H. Friedberg, A. J. Insel, L. E. Spence, “ Linear Algebra”, 4th Edition, PHI, 2003