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Unformatted text preview: eigenvector for softness, |w> for the eigenvector for white, and |b> as the eigenvector for black. So now we can use |h> and |s> as a basis for H and |w> and |b> as a basis for C (assuming the operators are 2x2). This means we can represent |w> and |b> as linear combinations of |h> and | s> and vice versa. |w> and |b> are not eigenvectors for H (as they are a linear combination of both |h> and |s>), so this means that there is no eigenvalue for |w> and |b>, which means that there is no definite hardness value, which is the mathematical representation of superposition. The same is true with |h> and |s> with respect to C. So hardness and color, in a sense, are incompatible qualities....
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- Fall '08