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By Li J., Su Y., Zhu L.

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15 First Eigenvector Second Eigenvector Third Eigenvector 0. 1: First three eigenvectors from NCS and Munsell spectral database Distribution of Munsell chips 12 10 1. Eigenvector 8 6 4 2 0 4 4 2 2 0 0 −2 −2 −4 3. Eigenvector −4 2. 2. We continue the discussion about the spaces of admissible and realizable spectra. In conventional chromaticity spaces, the realizable boundary is the well-known spectrum locus (see [Wyszecki and Stiles, 1982, page 125]). The admissible boundary is an inner boundary where most spectra in the database are located.

8) with a unit vector u = (uk )K . 9) σ Proof From the definition it follows: σ = s, b0 > C0 s, 1 > 0 where 1 is the function that has constant value one on the whole interval I. Next K define u = (uk )K k=1 as the unit vector in Eq. 8 and bu = k=1 uk bk . From the second property of the conical operator we find that | s, bu | ≤ C2 s, 1 . 10) < σ C0 s, 1 C0 Eq. 9 shows that the coordinate vector space of nonnegative signals with respect to a conical basis has a salient convex cone structure and is bounded.

9) σ Proof From the definition it follows: σ = s, b0 > C0 s, 1 > 0 where 1 is the function that has constant value one on the whole interval I. Next K define u = (uk )K k=1 as the unit vector in Eq. 8 and bu = k=1 uk bk . From the second property of the conical operator we find that | s, bu | ≤ C2 s, 1 . 10) < σ C0 s, 1 C0 Eq. 9 shows that the coordinate vector space of nonnegative signals with respect to a conical basis has a salient convex cone structure and is bounded. In the following, we will discuss the topology and boundaries of a coordinate vector space of nonnegative signals in this conical system.

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