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Discussion :: GATE Mathematics

  1. Let V = ℂ2 be the vector space over the field of complex numbers and B{(1, i), (i,1)}be a given ordered basis of V. Then for which of the following, B* = {f1, f2}is a dual basis of B over ℂ?
    2. A.
    f1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (z1 + iz2)
    B.
    f1(z1, z2) = 1/2 (z1 + iz2), f2(z1, z2) = 1/2 (iz1 + z2)
    C.
    f1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (-iz1 + z2)
    D.
    f1(z1, z2) = 1/2 (z1 + iz2), f2(z1, z2) = 1/2 (-iz1 - z2)

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    Answer : Option C

    Explanation :

    -NA-

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