### Curriculum

### Title-Linear Algebra (Code-09010602)

S.No | Unit | Contents | Learning Objective | Teaching Guidelines | Methodology | Time
(Hrs) |

1 | One | 1. Vector Spaces, Subspaces, sum and direct sum of subspaces, Linear span
2. Linearly dependent and independent 3. Finitely generated vector space &Existence theorem 4. Finite dimensional vector spaces 5. Invariance of no. of elements of basis set, Dimensions 6. Quotient space and its dimension |
To study Vector Spaces, its subspaces, basis and quotient spaces | Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests |
12 |

2 | Two | · Homomorphism and isomorphism of vector spaces
· Linear transformations and linear form · Dual spaces, Bidual spaces · Null space, Range space of a linear transformation, Rank & Nullity theorem · Algebra of linear transformations · Minimal polynomial of linear transformation · Singular & Non –Singular linear transformation · Matrix of a linear transformation, Change of basis · Eigen values and Eigen vector of linear transformations |
To study Homomorphism of vector spaces and Algebra of Linear transformation | Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests |
22 |

3 | Three | · Inner product spaces
· Cauchy Schwarz inequality · Orthogonal vectors, orthogonal complements · Orthogonal sets and basis · Bessel’s inequality for finite dimensional vector spaces · Gram-Schmidt Orthogonalization process |
To study inner Product Spaces | Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests |
10 |