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
 Hagar
 Linear Algebra, Vector Space, state vector, Andrew Dixon, Seta Degann, Stephen Beckley

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