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richyw

  • 3 years ago

show that \(\left| |\mathbf{a}|-|\mathbf{b}|\right| \leq |\mathbf{a}-\mathbf{b}|,\quad\forall\:\mathbf{a,b}\in\mathbb{R}^n\)

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  1. slaaibak
    • 3 years ago
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    (a - b)^2 = a^2 - 2ab + b^2 >= a^2 - 2|a||b| + b^2 = |a|^2 - 2|a||b| + |b|^2 so, (a - b)^2 >= |a|^2 - 2|a||b| + |b|^2 which leads to: (a - b)^2 >= (|a| - |b|)^2 ----> |a - b| >= ||a| - |b||

  2. richyw
    • 3 years ago
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    thanks!

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