Question: Suppose a linear transformation L: Rn Rn is represented by a symmetric matrix with respect to the standard basis e1,..., en. (a) Prove that

Suppose a linear transformation L: Rn → Rn is represented by a symmetric matrix with respect to the standard basis e1,..., en.
(a) Prove that its matrix representative with respect to any orthonormal basis u1,..., un is symmetric.
(b) Is it symmetric when expressed in terms of a non-orthonormal basis?

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