Show that the following inequalities hold for any x = (x1,...,xn) ? ?^n: max{|x1|,...,|xn|} ? |x| ? ?n max{|x1|,...,|xn|}.
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First, let's consider the left inequality: $$\max\{|x_1|, |x_n|\} < ||x||$$ We know that the Euclidean norm of a vector $x$ is defined as: $$||x|| = \sqrt{x_1^2 + x_2^2 + \cdots + x_n^2}$$ Since all the terms inside the square root are non-negative, we can say Show more…
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