EV5: add doenet basis visualization #881
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jkostiuk
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Dec 15, 2025
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| A basis for a Euclidean vector space can be used to create alternative coordinate systems, as can | ||
| be visualized by the following tool. |
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| A basis for a Euclidean vector space can be used to create alternative coordinate systems, as can | |
| be visualized by the following tool. | |
| A basis for a Euclidean vector space can be used to create alternative coordinate systems. This is visualized in the following interactive. As you drag the vector <m>\vec{v}</m> around the plane, the interactive shows how <m>\vec{v}</m> is expressed as a linear combination of the basis vectors <m>\vec{e}_1</m> and <m>\vec{e}_2</m>. If you click the toggle for the custom basis <m>\{\vec{b}_1,\vec{b}_2\}, the interactive will now show how to express the vector <m>\vec{v}</m> as a linear combination of the vectors <m>\vec{b}_1</m> and <m>\vec{b}_2</m>. You may also drag the vectors <m>\vec{b}_1</m> and <m>\vec{b}_2</m> to see how the results vary with different choices of custom bases. |
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@StevenClontz I like the interactive a lot. I think a caption that describes what the interactive does would be helpful. I've provided a suggestion for your review.
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This provides a little Doenet.org interactive to explore how bases form alternative coordinate systems.