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Question 5.E.3.8: Explain why the Frobenius matrix norm on C^n×n must satisfy ......

Explain why the Frobenius matrix norm on \mathcal{C}^{n×n} must satisfy the parallelogram identity.

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(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)

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