# Change of Basis in 2D

This application shows the connection between the coordinate vectors for a point in the standard basis and another basis.

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http://demonstrations.wolfram.com/ChangeOfBasisIn2D/
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Publisher:
Wolfram Demonstrations Project
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### connects visual and algebraic insights about bases

The user selects a point $P$ in $\mathbf{R}^2$ by dragging with the mouse. The coordinates of $P$ in the standard basis are given along with its coordinates in a second basis, which are calculated using the change-of-basis matrix. The determinant of the transformation is also shown, but its use is not explained.

### works as claimed, but could use better explanations

This applet does what it claims but some additional explanation from the author would make it more useful. For example, the author states that the determinant of the input matrix is a "crucial quantity" but doesn't say why.