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Vector subtraction

a.k.a.

• Vector difference

Define

… in terms of the additive inverse of vector addition as

\[\begin{equation*}
  \vec{u} - \vec{v} = \vec{u} + (-\vec{v}),
\end{equation*}
\]

where	\(\vec{u}, \vec{v}\)	are the terms,
	\(\vec{u} - \vec{v}\)	is the difference.

Discuss

• Algebraic properties

  … are that of vector addition.

Implement

… in Scheme as

• my-vector-subtract

  (define (my-vector-subtract vector . vectors)
    (if (null? vectors)
        vector
        (my-vector-add vector
                       (my-vector-additive-inverse
                        (apply my-vector-subtract
                               vectors)))))
  

  in terms of my-vector-add.

• my-vector-additive-inverse

  (define (my-vector-additive-inverse vector)
    (my-vector-scale vector -1))
  

  in terms of my-vector-scale.