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∥∞.

匿名用户 最后更新于 2021-12-01 19:07 数学类Mathematics

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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