clift
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Bases and Coordinates in R2
This applet demonstrates the concept of coordinate vectors in $\mathbb R^2$ A basis $\mathcal B$ of a vector space $V$ is a linearly independent spanning set. One useful feature of a basis is that it gives rise to a way of writing coordinates on $V$. Any vector $\mathbf v \in V$ can be written uniquely […]melbapplets.ms.unimelb.edu.au/2024/04/05/bases-and-coordinates-in-r2
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Visualising the Gram-Schmidt Algorithm
This applet demonstrates the Gram-Schmidt algorithm performed in $\mathbb R^3$. The Gram-Schmidt algorithm converts a basis of an inner product space into an orthonormal basis. It does this by building up the orthonormal basis one vector at a time. For each vector in turn, we remove any component that is parallel to the vectors which […]melbapplets.ms.unimelb.edu.au/2024/04/05/visualising-the-gram-schmidt-algorithm
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Visualising linear transformations in R2
This applet shows the geometric effect of a linear transformation $T: \mathbb R^2 \to \mathbb R^2$. You can type a matrix $M$ on the right hand side of the applet, and then click Play to see how the vertices of a triangle are transformed when multiplying by $M$. Other resources: Geogebratube page for this appletmelbapplets.ms.unimelb.edu.au/2024/03/25/visualising-linear-transformations-in-r2
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Visualising linear transformations in R3
This applet shows the geometric effect of a linear transformation $T$ in $\mathbb R^3$. You can type a 3×3 matrix $M$ on the right hand side of the applet, and then click Play to see how the vertices of a cube are transformed when multiplying by $M$. Can you see if the corresponding transformations are […]melbapplets.ms.unimelb.edu.au/2024/03/25/visualising-linear-transformations-in-r3