Question is from Artin's Algebra, p. 263.
If $A$ is the matrix of a symmetric bilinear form, prove or disprove: The eigenvalues of $A$ are independent of the choice of basis.
I suspect the result is true.
Real & Symmetric $\Rightarrow$ Hermitian
Then by Corollary (4.12) the matrices which represent the same hermitian form are $= QAQ^*$, where $Q\in \operatorname{GL}_n(\mathbb{C})$.
Does this mean that all of these matrices are similar? If so I would be done since similar matrices have the same eigenvalues.