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Sage LTB: changed "to be" to "is" to make grammatical sense (Jenna) #28

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Sage LTB: changed "to be" to "is" to make grammatical sense (Jenna) #28

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2 changes: 1 addition & 1 deletion src/section-LT.xml
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Expand Up @@ -968,7 +968,7 @@ Codomain: Vector space of dimension 4 over Rational Field
</output>
</sage>

Notice that there is no requirement that the list of images (in Sage or in <acroref type="theorem" acro="LTDB" />) to be a basis. They do not even have to be different. They could all be the zero vector (try it).<br /><br />
Notice that there is no requirement that the list of images (in Sage or in <acroref type="theorem" acro="LTDB" />) is a basis. They do not even have to be different. They could all be the zero vector (try it).<br /><br />
If we want to use an alternate basis for the domain, it is possible, but there are two caveats. The first caveat is that we must be sure to provide a basis for the domain, Sage will give an error if we the proposed basis is not linearly independent and we are responsible for providing the right number of vectors (which should be easy).<br /><br />
We have seen that vector spaces can have alternate bases, which prints as a <q>user basis.</q> Here will provide the domain with an alternate basis. The relevant command will create a subspace, but for now, we need to provide a big enough set to create the entire domain. It is possible to use fewer linearly independent vectors, and create a proper subspace, but then we will not be able to use this proper subspace to build the linear transformation we want.
<sage>
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