View source for pu'e'ei

==== valsi ====
pu'e'ei
==== type ====
experimental cmavo
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Mon Jan  9 09:02:38 2023
 
== English ==
=== Definition #73114 - Preferred ===
 
==== selma'o ====
VUhU3
==== definition ====

mekso binary operator: generate span; outputs span MATH
 $(X_1, X_2)=$
 
<span class="MATH">(<i>X</i><sub>1</sub>, <i>X</i><sub>2</sub>) =</span> span MATH
 $_{X_2}(X_1)$
 
<span class="MATH"><sub>X<sub>2</sub></sub>(<i>X</i><sub>1</sub>)</span>; set of all (finite) sums of terms of form <span class="MATH"><i>cv</i></span>, where <span class="MATH"><i>v</i></span> is an element of algebraic structure <span class="MATH"><i>X</i><sub>1</sub></span> (wherein scalar multiplication and summation is defined), and <span class="MATH"><i>c</i></span> is a scalar belonging to ring <span class="MATH"><i>X</i><sub>2</sub></span>.

==== notes ====

For example, the span of vectors <span class="MATH"><i>v</i><sub>1</sub></span> and <span class="MATH"><i>v</i><sub>2</sub></span> in vector space <span class="MATH"><i>V</i></span> over the field of exactly all real numbers R has <span class="MATH"><i>X</i><sub>1</sub> =</span> Intersect<span class="MATH">(<i>V</i>,</span> Set MATH
 $(v_1, v_2))$
 
<span class="MATH">(<i>v</i><sub>1</sub>, <i>v</i><sub>2</sub>))</span> and <span class="MATH"><i>X</i><sub>2</sub> =</span> R and yields output Set MATH
 $(c_1 v_1 + c_2 v_2 : c_i$
 
<span class="MATH">(<i>c</i><sub>1</sub><i>v</i><sub>1</sub> + <i>c</i><sub>2</sub><i>v</i><sub>2</sub> : <i>c</i><sub>i</sub></span> in R for all<span class="MATH"><i>i</i>)</span>, where scalar multiplication and vector addition are as defined in <span class="MATH"><i>V</i></span>.

==== gloss words ====

<ul><li>[[natlang/en/linear combination|linear combination]]</li><li>[[natlang/en/linear superposition|linear superposition]]</li><li>[[natlang/en/span|span ; algebra]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
1
     
==== time ====
Mon Jan  9 09:08:49 2023



<br/><font size="+1">Examples</font>
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=== Etymology ===