Explain why the Frobenius matrix norm on \mathcal{C}^{n×n} must satisfy the parallelogram identity.
(a) As shown in Example 5.3.2, the Frobenius matrix norm \mathcal{C}^{n×n} is generated by the standard matrix inner product (5.3.2), so the result on p. 290 guarantees that ||\star||_F satisfies the parallelogram identity.
〈A|B〉 = trace (A^T B) and 〈A|B〉 = trace (A^∗ B) (5.3.2)