Change of Basis
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This example illustrates the concept of change of basis. Change of basis is an important concept in linear algebra, where transforming the basis simplifies the representation of vectors. It uses buttons, points, and images to demonstrate how to change the representation of vectors by transforming the basis. Suitable for high school and above students learning linear algebra and geometric transformations.
GeoGebra Commands & Parameters
Point A(-2.21219987440261, -1.6797962595917642)Point B(2.787800125597391, -1.6797962595917642)Point C(3.997128304256554, -1.2425072020869514)Point D(8.577128304256554, -1.0225072020869517)Point E(4.23148678297378, 2.4704503867649525)Point F(8.071486782973782, 2.4904503867649526)Point G(4.7742566085131095, -3.4314978159424405)Point H(7.7342566085131095, -3.3914978159424405)Point I(9.47042897439646, -1.817724120742933)Point J(15.47042897439646, -1.817724120742933)Numeric Show(0)
AI Drawing Prompt Reference
Draw a graph with multiple points that are roughly linearly arranged or form several straight lines, distributed in two horizontal directions, some points below and some above, showing the change of vector representation under different bases, with the spatial relationship of points illustrating the concept of basis transformation.
The prompt above was compiled from the original drawing commands and is for reference only.