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 <h2 id="plan">Plan</h2>
 <ul>
 <li>2.1</li>
 </ul>
 <h2 id="linear-transformation">2.1 Linear Transformation</h2>
 <ul>
 <li>Recall a linear transformation is a map T such that T(x + y) = T(x) + T(y) and T(cx) = cT(x).
 <ul>
 <li>We can also apply this to a general linear combination.</li>
 <li>Differentiate and integration are examples.</li>
 <li>Reflections, projections (there are multiple versions)</li>
 <li>Translation is not an example.</li>
 <li>Identity and zero transformations</li>
 </ul></li>
 <li>null space and kernel, range and image</li>
 <li>Theorem: these are subspaces</li>
 <li>image of subspaces T(W)</li>
 <li>prove rank-nullity. Pick a basis for null space and extend.</li>
 <li>One-to-one</li>
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Collaborative Calculation and Data Science

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