It is wrong $\pmatrix{0&1\cr1&0\cr}$ and $\pmatrix{2&1\cr0&-1/2\cr}$ are congruent but the first one has $1$ and $-1$ as eigen values and the second one has $2$ and $-1/2$ as eigen values.
It is wrong $\pmatrix{0&1\cr1&0\cr}$ and $\pmatrix{2&1\cr0&-1/2\cr}$ are congruent but the first one has $1$ and $-1$ as eigen values and the second one has $2$ and $-1/2$ as eigen values.