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Talabar Find the orthogonal complement of a subspace. Lines, planes, hyperplanes in Rn. Describe the transformation of the matrix of a linear operator under a change of basis. State the polar decomposition theorem for nonsingular operators. Give example of the canonical form of an antisymmetric matrix. Use the Gram matrix to compute the length of line segment, the area of a parallelogram and the volume of a parallelepiped.
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