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scalar multiplication

Rescaling every entry of a vector by the same number.

Scalar multiplication rescales every entry of $\mathbf u$ by the same number $c$ : $c\mathbf u = (cu_1, cu_2)$ . It points the same direction as $\mathbf u$ when $c>0$ , the exact opposite direction when $c<0$ , and $|c|$ controls how much longer or shorter the arrow gets.

See also

vector addition linear combination

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