Paper-I
Section-A
Linear Algebra
Vector, space, linear dependance and independance, subspaces, bases, dimensions. Finite dimensional vector spaces. Matrices, Cayley-Hamiliton theorem, eigenvalues and eigenvectors, matrix of linear transformation, row and column reduction, Echelon form, eqivalence, congruences and similarity, reduction to canonical form, rank, orthogonal, symmetrical, skew symmetrical, unitary, hermitian, skew-hermitian forms their eigenvalues. Orthogonal and unitary reduction of quadratic and hermitian forms, positive definite quardratic forms.