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Unformatted text preview: representation (Hint: The eigenvectors are orthogonal to each other. For complex eigenvectors, remember that the normalization is defined as A*A where A* is the complex conjugate). 1 c. Construct the similarity transformation matrix from the eigenvectors and determine . For the case where the eigenvectors are complex, take linear combinations to yield 1 eigenvectors in real space. is the adjoint of divided by the determinant. See pg 424 in Cotton for the definition of an adjoint. d. Using and 1 block-diagonalize the matrices in Part (a) and calculate the characters of the irreducible representations for the given basis. e. To what irreducible representations do the F atom basis functions belong? f. Complete the D 3h character table using the algebraic rules governing irreducible representations. Show work....
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