Exams¶

The course has two exams one is internal of 15 marks, while the other is final worth 70 marks. Rest marks are part of continuous assesment that belongs to attendence, seminar and assignments.

• Unit I

  • Gaussian Elimination (Problems)
  • Matrix of Linear Transformation (Theorem + Proof + Problems)

• Unit II

  • Hermitian, Skew Hermitian and Unitary Matrix (Definition + Examples + Related Theorems)
  • Inner Product Space (Definition + Problems)
  • Gram-Schmidt Orthogonalization (Theorem + Problems)
  • Self-adjoint operators

• Unit III

  • Similar Matrices (Definition + Problems)
  • Invariant Subspace (Definition + Problems + Related Theorems)
  • Triangulizaton (Defintion + Condition of Trinagulization)
  • Nilpotent Transformation (Defintion + Example)
  • Primary Decomposition Theorem (Statement + Proof + Problems)
  • Jordan Form of Matrix (Problems)
  • Rational Form of Matrix (Problems)

• Unit IV

  • Bilinear Form (Defintion + Problems)
  • Algebra of bilinear forms (Statement + Proof)
  • Degenerate and Non-degenerate bilinear forms (Defition + Problems)
  • Alternating Forms (Defition + Problems)

• Unit V

  • Symmetric and Skew-Symmetric bilinear forms (Definition + Problems + Related Theorems)
  • Quadratic Form (Defintion + Problems)
  • Sylvester's Theorem (Statement + Proof + Problems)
  • Invariants of quadratic forms (Defintion + Problems)

1. Internal Exam¶

To download the question of last internal exam click here.

2. Final Exam¶

Final exam divided in three groups. The questions are organized in three groups as follows: