1- Vector Spaces ( सदिश समष्टियां ) 2- Linear Combination of Vectors ( सदिशों का एकघात संचय ) 3 - Basis and Dimensions ( आधार एवं विमाएँ ) 4- Linear Transformations ( रैखिक रूपान्तरण ) 5- Eigen Values and Eigen Vectors ( आइगेन मान एवं आइगेन सदिश ) -------------------------------------------------------------------------------------------------------------------- Vector Spaces : Definition and examples of a vector spaces, subspaces, sum and direct sum of subspaces, linear span, linear dependence, Independence and their basic properties, Basis, finite dimensional vector spaces, Existence theorem for basis, invariance of the number of elements of a basis set, Dimension, existence of complimentary subspace of a subspace of a finite dimensional vector space, dimension of sums of subspaces, quotient space and its dimension. ==================================================== Linear transformations : Linear Transformations and their representation as matrices, the algebra of linear transformations, the Rank-Nullity theorem, ============================================== Eigen values and Eigen vectors, similar matrices, equivalent matrices, Similarity of Linear transformations ================================================================== NOTE : This course is valid only with registered mobile numbers. Videos by-- Dr. Kaur Singh Dhounsi M.Sc., Ph.D. ( Mathematics ) Address- 45-D ,Setia Colony Sriganganagar , Rajasthan-335001 Mob- 9414989144