# Applied Linear Algebra – EE5120

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 :**

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