Main Page > BS Mathematics (Morning) (After 2 Years ADP Mathematics) > MATH-308 Rings and Vector Spaces
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MATH-308 Rings and Vector Spaces
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Ring Theory Definition and example of rings Special classes of rings Fields Ideals and quotient rings Ring homomorphisms Prime and maximal ideals Field of quotients Vector Spaces Vector spaces, subspaces Linear combinations, linearly independent vectors Spanning set Bases and dimension of a vector space Homomorphism of vector spaces Quotient spaces Linear Mappings Mappings, linear mappings Rank and nullity Linear mappings and system of linear equations Algebra of linear operators Space L( X, Y) of all linear transformations Matrices and Linear Operator Matrix representation of a linear operator Change of basis Similar matrices Matrix and linear transformations Orthogonal matrices and orthogonal transformations Orthonormal basis and Gram Schmidt process Eigen Values and Eigen Vectors Polynomials of matrices and linear operators Characteristic polynomial Diagonalization of matrices Dual Spaces Linear functionals Dual space Dual basis Annihilators |
| Credit hours/ Marks:- 3 |
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