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Subject Syllabus

CY-401 - Introduction to Linear Algebra

CSCY • SEMESTER-4

Course Modules

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Direct sum of a vector space Dual Spaces Annihilator of a subspace Quotient Spaces Algebra of Linear transformations

Characteristic values and characteristic polynomials diagonalizable transformations annihilating polynomials Cayley-Hamilton theorem invariant subspaces and triangular form simultaneous triangularization and diagonalization direct sum decompositions invariant direct sums primary decomposition theorem

Adjoint of a linear transformation Inner product spaces Eigen values and eigenvectors of a linear transformation Diagonalization Invariant subspaces Inner product spaces, adjoints, unitary and normal transformations spectral Theorem Jordan canonical form

Canonical forms Similarity of linear transformations Reduction to triangular forms Nilpotent transformations Primary decomposition theorem Jordan blocks and Jordan forms Invariants of linear transformations

Hermitian, Self adjoint, Unitary and normal linear transformation Symmetric bilinear forms skew symmetric bilinear forms Group preserving bilinear forms