Prove the following Matrix Norms properties For any matrix A ∈Cm×n, we have
1- ||AH||1 = ||AT||1 =∥A∥∞
2- ||AH||2 = ||AT||2 =∥A∥2
3- ||AHA||2 =∥A∥22
4- ∥A∥22 ≤ ∥A∥1 ∥A∥∞.
Example 4 For any matrix A ECMXN, we have ||A" ||| = ||A" || = || A||50 ||44||2 = ||A7 || 2 = || 1 | 2 ||AⓇA||2 = ||A||2? || A||2 < ||A|| | ||A||.
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