Review of algebra of matrices & elementary transformations, Rank of a matrix, inverse of a matrix by Gauss-Jordan method, normal form of a matrix, Solution of system of algebraic simultaneous equations, Linear dependent and Linear independent vectors. Eigen values and Eigen vectors, Eigen values and Eigen vectors of: Symmetric, Skewsymmetric, Hermitian, Skewhermitian, Unitary and Normal matrix, Algebraic and Geometric multiplicity, Diagonalization, Spectral theorem for real symmetric matrices, Application of Quadratic forms.
Vector Space :
Vectors in Rn and its properties, Dot product, Norm and Distance properties in Rn, Pythagorean theorem in Rn ,Definition and Examples of vector spaces, Vectorsubspace, Linear Independence and dependence ,Linear span of set of vectors, Basis of subspaces, Extension to basis.
Linear Transformation :
Definition and basic properties, Types of linear transformation(Rotation,reflection,expansion,contraction,shear,projection),Matrix of linear transformations,Change of basis and similarity, Rank nullity theorem
Infinite Series :
Definition, Comparison test, Cauchy’s integral test, ratio test, root test, Leibniz’s rule for alternating series, power series, range of convergence, uniform convergence.
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