Syllabus
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Course Code: MT-501 Course Name: (A) Linear Algebra |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Vector spaces. Subspaces. Algebra of subspaces. Quotient space. Linear combination of vectors. Linear span. Linear dependence and independence of vectors. Bases and dimension. Dimension of subspaces. Linear transformations. Null space. Range space. Matrix representation of a linear transformation. Rank and nullity of a linear transformation. Algebra of linear transformations. |
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| 2 | Isomorphism of vector spaces, Isomorphism theorems. Dual and second dual of a vector space, Transpose of a linear transformation, Eigen vectors and eigen values of a linear transformation, Characteristic polynomial and Cayley-Hamilton theorem, Minimal polynomial. | |
| 3 | Inner product spaces and orthogonality, Cauchy-Schwarz inequality, Gram-Schmidt orthog-onalisation, Diagonalisation of symmetric matrices. | |
| 4 | Adjoint of a linear operator; Hermitian, unitary and normal linear transformations; Jordan canonical form, Triangular form, Trace and transpose, Invariant subspaces. | |
