CY-401 · Introduction to Linear Algebra/Official Syllabus
Introduction to Linear Algebra (CY-401) - Official Syllabus
1
Unit 1
Direct sum of a vector space
- Direct sum of a vector space
- Dual Spaces
- Annihilator of a subspace
- Quotient Spaces
- Algebra of Linear transformations
2
Unit 2
Characteristic values and characteristic polynomials
- Characteristic values and characteristic polynomials
- diagonalizable transformations
- annihilating polynomials
- Cayley-Hamilton theorem
- invariant subspaces and triangular form
- simultaneous triangularization and diagonalization
- direct sum decompositions
- invariant direct sums
- primary decomposition theorem
3
Unit 3
Adjoint of a linear transformation
- Adjoint of a linear transformation
- Inner product spaces
- Eigen values and eigenvectors of a linear transformation
- Diagonalization
- Invariant subspaces
4
Unit 4
Canonical forms
- Canonical forms
- Similarity of linear transformations
- Reduction to triangular forms
- Nilpotent transformations
- Primary decomposition theorem
- Jordan blocks and Jordan forms
- Invariants of linear transformations
5
Unit 5
Hermitian, Self adjoint, Unitary and normal linear transformation
- Hermitian, Self adjoint, Unitary and normal linear transformation
- Symmetric bilinear forms
- skew symmetric bilinear forms
- Group preserving bilinear forms
Reference Books
- Finite dimensional vectors paces — P. Halmos — Springer
- Linear algebra — Peter D. Lax — Wiley student edition
- A course in algebra, Graduate text in Mathematics, volume 56 — E.B. Vinberg — AMS
- Linear algebra — M. Thamban Nair, Arindama singh — Springer
- Linear Algebra — K. Hoffman, R. Kunze — Prentice Hall of India — 2nd Edition
- Linear Algebra Done Right — S. Axler — Springer UTM — 2nd Edition
Go to where you left off?
Quick Add to Notes
Save questions, your own notes and screenshots into notes filed by unit. It takes a free account.
Create free accountHave an account? Log in
Notes Panel