Syllabus
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Course Code: B-MAT 503 Course Name: 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. Matrix representation of a linear transformation. Rank and nullity of a linear transformation. | |
| 2 | Transpose of a linear transformation, Eigen vectors and eigen values of a linear transformation, Characteristic polynomial and CayleyHamilton theorem, Minimal polynomial | |
| 3 | Inner product spaces and orthogonality, CauchySchwarz inequality, GramSchmidt orthogonalization, Diagonalization of symmetric matrices. | |
| 4 | Adjoint of a linear operator; Hermitian, unitary and normal linear transformations; Triangular form, Trace and transpose. | |
