**This workshop will aim to touch upon some of these topics **

**Foundation**

Vector Spaces, Subspaces, Basis, Linear transformation, Quotient Space, Rank-nullity theorem, Matrix representations, Inner product Spaces

**Diagonalization**

Eigenvalues and Eigenvectors; Geometric and Algebraic multiplicities, characteristic equation, spectral theorem for a symmetric operator in a f.d. inner

product space. Structure of a single linear transformation, Algebra of Projections, Equivalence of Matrices and Similarity of Matrices

**Isomorphism Theorems
**

Isomorphism theorems, Linear Functionals, Dual bases, Operator Adjoints, norm, orthogonal direct sums,The Riesz Representation Theorem

**Algebraic Structures
**

Groups, Subgroups, Ring, Ideals, Quotient Rings, Maximal Ideals, Quotient fields, PIDs, UIDs, Fields and Algebras

**Module
**

Modules, Submodules, Homomorphisms , Quotient Modules, The Cyclic Decomposition of a Primary Module

__Workshop Cloud __