Negative Tristimulus Values

Sometimes when it is impossible to match a color $L$ by superimposing (mixing) the given primaries $P_j,\;\;\;(j=1,2,3)$ as described above, it is possible to still match the color in a different way. For example, the mixture of one or two primaries with the given color $L$ may be matched by the mixture of the remaining primaries:

• Mixing one primary with the given color
  
  $$[L]+ A_1(L) [P_1] \equiv A_2(L) [ P_2 ]+ A_3(L) [ P_3]$$
  
  
  with the tristimulus values correspondingly defined as
  
  $$T_1(L)=\frac{-A_1(L)}{A_1(W)}\;\;\;\;\;\; T_2(L)=\frac{A_2(L)}{A_2(W)}\;\;\;\;\;\; T_3(L)=\frac{A_3(L)}{A_3(W)}$$
  
  

• Mixing two primaries with the given color
  
  $$[L]+ A_1(L) [ P_1] + A_2(L) [ P_2 ]\equiv A_3(L) [ P_3 ]$$
  
  
  with the tristimulus values correspondingly defined as
  
  $$T_1(L)=\frac{-A_1(L)}{A_1(W)}\;\;\;\;\;\; T_2(L)=\frac{-A_2(L)}{A_2(W)}\;\;\;\;\;\; T_3(L)=\frac{A_3(L)}{A_3(W)}$$