Skip to main content\(\newcommand{\avec}{{\mathbf a}}
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\)
An interactive diagram with four sliders arranged in a
\(2\times2\) array, which allow the reader to define a matrix
\(A\text{.}\)
On the left below the sliders is a standard
\(1\times1\) coordinate grid and axis, along with the unit circle, and a unit vector
\(\xvec\) that can be moved around the unit circle.
On the right below the sliders is a standard
\(1\times1\) coordinate grid and set of axes. The unit circle on the left is transformed by the matrix into an ellipse on the right. As the vector
\(\xvec\) on the left is moved around the unit circle, the vector
\(A\xvec\) moves around the ellipse. There is a second vector, which is a unit vector pointing in the same direction as
\(A\xvec\text{.}\) Also shown is a rectangle whose height represents
\(\len{A\xvec}\text{,}\) the length of
\(A\xvec\text{.}\)
Instructions.
You may choose a
\(2\times2\) matrix
\(A=\begin{bmatrix}
a \amp b \\
c \amp d \\
\end{bmatrix}\) using the four sliders at the top of the diagram. On the left, you may vary the red unit vector
\(\xvec\) by clicking in the head of the vector.
