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Unit 2: Vector Space and Linear Transformation
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Syllabus
Unit 1: Introduction to Matrix Algebra
- Echelon Form of a Matrix
- The Rank of a Matrix
- Determinant and Inverse of a Matrix
- Solution of System of Homogeneous & Non- Homogeneous Equations: Gauss Elimination
- Solution of System of Homogeneous Equations: Gauss Jordan Method
Unit 2: Vector Space and Linear Transformation
- Vector Space
- Sub-spaces
- Linear Combinations
- Linear Span
- Convex Sets
- Linear Independence Dependence
- Basis & Dimension
- Linear Transformation on Finite Dimensional
- Vector Spaces
- Inner Product Space
- Schwarz Inequality
- Orthonormal Basis
- Gram-schmidt Orthogonalization Process
Unit 3: Eigenvalue and Eigenvector
- Characteristic Polynomial
- Cayley Hamilton Theorem
- Eigen Value and Eigen Vector of a Matrix
- Eigenspaces
- Diagonalization
- Positive Definite Matrices
- Applications to Markov Matrices