Matrix Algebra Topics - Linear Algebra - Gate Syllabus 2012

Gate Syllabus 2012 for Mechanical Engineering

Engineering Mathematics

Linear Algebra

Matrix Algebra Topics

1. Gauss Jordan Method (Obtain Inverse using elementary row Transformations).
2. Rank of a Matrix
3. Solution of a System of Linear equations
4. Unique Solution (AX=B condition)
5. Vectors
6. Linear Dependence and Linear Independence of vectors
7. Linear Transformations
8. Orthogonal Transformations
9. Characteristic equation
10. Eigen Vectors
11. Properties of Eigen Values
12. Cayley Hamilton Theorem
13. Reduction to Diagonal Form
14. Calculations of Powers of a Matrix
15. Similar Matrices
16. Theory on Similar Matrices
17. Quadratic Forms
18. Linear transformations of a quadratic forms
19. Canonical Form
20. Index and signature of quadratic Form
21. Definite Semi-Definite and Indefinite Real quadratic forms
22. Law of inertia of Quadratic form
23. Reduction to canonical form by orthogonal transformation. 

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