# Vector Transformations and Eigenvectors of 2×2 Matrix

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This Demonstration shows the transformation represented by a matrix applied to a vector . The vector is transformed to a new vector , shown in color. If the vector is an eigenvector of , then is simply scaled by , the eigenvalue, without changing direction (except the direction is reversed if .) Color-coded formulas show the calculation of the inverse, determinant and new vector , as well as the eigenvectors of .

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Contributed by: Timothy Newlin (August 2020)

(United States Military Academy West Point)

Open content licensed under CC BY-NC-SA

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