Topics covered
Foundations of Linear Algebra
- Group, Field
- Preliminary matrix operations
- System of linear equations
- Vector Space
- Subspace
- Linear span
- Basis and Dimension of a vector space
- Operations on subspaces of a vector space
- Linear Transformation
- Rank - Nullity Theorem
- Change of Basis Matrix
- Applications
Inner Product Spaces
- Inner Product spaces
- Cauchy - Schwarz inequality
- Orthonormal Basis
- Gram - Schmidt orthogonalization process
- Orthogonal Complement of a subspace
- Eigen Values and Vectors of linear operations and square matrices
- Cayley - Hamilton Theorem
- Minimal Polynomial
- Jordan Canonical Form
- Special Matrices
- Quadratic Forms
- Eigen Values of special matrices