Week 05: Introduction to Vector Spaces,examples and preliminary results
Anton H., Rorres C. , Elementary Linear Algebra: Applications Version, 11th Edition, John Wiley and sons, 2010.
Page No: 183-190
Course Material
- Week 01:Representation of Linear equations in Matrix form, Operations on Matrices
- Week:02 Echelon and Reduced Echelon form, Solution of linear system, Gauss-Jordan method, Gaussian elimination
- Week 03: Inverse of a matrix (by elementary row operations), Determinants and their Computations
- Week 04:. Definition of higher order determinants. Properties of Determinants, Expansion of determinants
- Week 05: Introduction to Vector Spaces,examples and preliminary results
- Week 06: Subspace : Definition ,Examples and related results
- Week 07: Linear combination of a set of vectors,Linearly independent set of vectors: Definition ,examples and results
- Week 08: Basis of a Vector space:Definition ,examples and related results
- Week 09: Mid Term Exam
- Week 10 : Dimension of a vector space :Definition ,examples and related results
- Week 11: Change of Basis,Linear transformation ;Definition,Examples ,results
- Week 12: Null Space ,Basis for Solution space of Homogeneous System rank of Matrix
- Week 13: Kernel and Image of a linear transformation ,Rank and Nullity of Linear Transformation
- week 14 : Linear Transformations ,reflection ,projections homotheties, matrix of linear transforamtion
- Week 15: . Eigen-values and eigenvectors. Theorem of Hamilton-Cayley.
- Week 16 : Diagonalization ,Inner Product spaces with properties
- Week 17 ;Inner product Spaces:Projection,Cauchy inequality,Orthogonal and orthonormal basis. Gram Schmidt Process.
- Week 18 : Final Term Exam
- Chapters 18
- Department Mathematics(SCB)
- Teacher
Kiran Shaffee
