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• Vector spaces and Subspaces
• Bases and dimensions of vector spaces
• QUOTIENT SPACES
• CHANGE OF BASIS AND TRANSITION MATRICES
• LINEAR TRANSFORMATION AND MATRICES
• INNER PRODUCT SPACES AND ORTHOGONALITY
• ORTHOGONAL SUBSPACES
• RANK & NULLITY OF LINEAR TRANSFORMATION
• MID TERM EXAMS
• EIGEN VALUES AND EIGEN VECTORS
• CHARACTERISTICS EQUATIONS
• SIMILAR MATRICES
• DIAGONALIZATION OF MATRICES
• ORTHOGONAL & ORTHONORMAL MATRICES
• GRAMM SCHMIDT PROCESS OF ORTHOGONAIZATIONS
• DUAL SPACES
• ELIMINATION METHODS & SOLVING EQUATIONS FOR MATRICES
• FINAL TERM EXAMS