PUC lecturers recruitment 2012 CET syllabus for Mathematics Mathematics (Subject Code - 14) PAPER -1 Linear Algebra Vector space, bases, dimension of a finitely generated space, ‘Linear Transformations, Rank and nullity of a linear transformation, Cayley-Hamilton theorem, Eigenvalues and Eigen vectors. Matrix of a linear transformation, Row and Column reduction. Echelon form. Equivalence, Congruence and similarity. Reduction to canonical forms. Orthogonal, Symmetrical, skew-symmetrical, unitary, Hermitian and skew-Hermitian matrices-their eigenvalues, orthogonal and unitary reduction of quadratic and Hermitian forms. Positive definite quardratic forms, simultaneous reduction. Calculus:
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