How do I normalize a vector?

Great question ! Normal izing a vector is a common operation in linear algebra and machine learning . To normal ize a vector , you can use the following formula : \n $$ \ mathbf { x }' = \ frac {\ mathbf { x }}{\ |\ mathbf { x }\ | }$$ \n Where $\ mathbf { x }$ is the vector you want to normal ize , and $\ |\ mathbf { x }\ |$ is the magnitude ( or length ) of the vector . The resulting vector $\ mathbf { x }' $ has the same direction as $\ mathbf { x }$, but its magnitude is equal to 1 . \n For example , if you have a vector $\ mathbf { x } = ( 3 , 4 )$, you can normal ize it by div iding it by its magnitude : \n $$ \ mathbf { x }' = \ frac {\ mathbf { x }}{\ |\ mathbf { x }\ | } = \ frac {( 3 , 4 )}{ 5 } = \ frac { 3 }{ 5 }, \ frac { 4 }{ 5 }$$ \n Note that the magnitude of a vector is always non - negative , so the normal ized vector will also be non - negative . \n I hope this helps ! Let me know if you have any other questions . </s>