Statistics Solutions

[See] Angle between two nonnegative vectors. Let x and y be two nonzero n -vectors with nonnegative entries, i.e., each x_i ≥q 0 and each y_i ≥q 0

Question: Angle between two nonnegative vectors. Let $x$ and $y$ be two nonzero $n$ -vectors with nonnegative entries, i.e., each $x_{i} \geq 0$ and each $y_{i} \geq 0 .$ Show that the angle between $x$ and $y$ lies between 0 and $90^{\circ}$. Draw a picture for the case when $n=2$, and give a short geometric explanation. When (for general $n$ ) are $x$ and $y$ orthogonal?

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[See] Angle between two nonnegative vectors. Let x and y be two nonzero n -vectors with nonnegative entries, i.e., each x_i ≥q 0 and each y_i ≥q 0

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