Welcome
Topic Video Content
Vector Space Notes
Linear Subspace
Linear Dependent/Independent sets
Some Basic Inequalities
Metric Space
Review of metric space
Normed Vector Space
Convex Sets
Completeness property in NLS
Series convergence and completeness
Cantor intersection theorem
Finite dimension in NLS
Finte dimension and compactness
Equivalent Norms
Quotient normed linear space
Linear operator
Bounded Linear Transformation
Extension of Linear Operator
Compact Linear Operators
Linear Functionals
Dual Space
Example of Dual Space
Banach contraction principle and its applications
Hahn Banach Theorem
Application of Hahn Banach Theorem
Uniform boundedness theorem
Open Mapping Theorem
Closed Graph Theorem
Inner Product Space
Orthogonal & Orthonormal vectors
Best approximation in IPS
Gram-Schimdt orthogonalization
Some results in IPS
Total orthonormal sets
Functional representation of Hilbert Space
Adjoint operator
Self adjoint, unitary, and normal operator
Projection Operator
Strong and weak convergence
Lecture Notes PDF
Tutorial Sheets
Tutorial Sheet 1
Tutorial Sheet 2