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...Mathematics paper iii linear algebra and vector calculus unit spaces general properties subspaces combinatons of vectors span sum two dependence independence basis space finite dimensional dimension transformations operators null range transformation rank nullity as product invertible the matrix representation a adjoint or transpose sylvester s law characteristic values cayley hamilton theorem diagonalizable inner euclidean unitary norm length schwartz inequality othogonality orthonormal set complete gram schmidt orthogonalization process by j n sharma r vasista krishna prakasham mandir meerut kenneth hoffman ray kunze pearson education new delhi stephen h friedberg others published prentice hall international inc multiple integrals introduction concept plane curve line sufficient condition for existence integral area subset calculation double jordan change order integration limit variable in lengths curves surface areas expression course mathematical analysis shanti narayana p k mitta...