Empty sum

<h2 id="examples">Examples</h2>
<h3>Empty linear combinations</h3>
<p>In <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>, a basis of a vector space <i>V</i> is a linearly independent subset <i>B</i> such that every element of <i>V</i> is a <a href="/facts/Linear_combination/CVjL6kuN">linear combination</a> of <i>B</i>.
The empty sum convention allows the zero-dimensional vector space <i>V</i>={0} to have a basis, namely the <a href="/facts/Empty_set/ffEk3eA6">empty set</a>.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Empty_product/mj7nhGeD">Empty product</a></li>
<li><a href="/facts/Iterated_binary_operation/3yQuHKgU">Iterated binary operation</a></li>
<li><a href="/facts/Empty_function/CdReEKCh">Empty function</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Harper, Robert (2016). Practical Foundations for Programming Languages. Cambridge University Press. p. 86. ISBN 9781107029576. <a href="9781107029576" target="_blank">9781107029576</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>David M. Bloom (1979). Linear Algebra and Geometry. pp. 45. ISBN 0521293243. <a href="0521293243" target="_blank">0521293243</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Empty sum open-in-new

Empty sum