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[See] Suppose a mapping from R^2 to R^2 is defined by some 2x2 matrix W . Is the image of W spanned by the eigenvectors of W

Question: Suppose a mapping from \({{\mathbb{R}}^{2}}\) to \({{\mathbb{R}}^{2}}\) is defined by some 2x2 matrix W . Is the image of W spanned by the eigenvectors of W .

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