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GATE Mathematics 2013 Paper

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Question : 39

Total: 65

Let B be a real symmetric positive-definite n×n matrix. Consider the inner product on Rn defined by ❬X,Y❭=YtBX. Let A be an n×n real matrix and let T:Rn→Rn be the linear operator defined by T(X)=AX for all X∈Rn. If S is the adjoint of T, then S(X)=CX for all X∈Rn, where C is the matrix

B−1AtB
BAtB−1
B−1AB
At

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