in order of decreasing significance. That is, the first vector 

 describes the largest part of the variation, and subsequent 

 vectors describe smaller parts of the variability. 



' The question for our spectral iTieasuring problem is, 

 "Can the first three vectors describe our population of data v/ith 



sufficient accuracy?" The average curve and the first three 



2 



characteristic vectors for a population of algae curves are 



shovfii in Figure 3. The values of these curves are shov/n plotted 

 versus v/avelength . These vectors can be thought of as the "dyes" 

 v;hich combine to make up the various algae spectral curves. 

 These vector's fit the algae curves v/ith a standard error of .03. 

 Each of the spectral absorbance curves in the population can be 

 matched by combining the average curve and some amovint of each 

 of the three vectors. 



^A^ ^""a^ Yi*ViX+ Y2^V2^+ Y3*V3;i^ 

 A = the spectral absorbance curve / \ 



Yi3Y2)^^, = the amounts of the vectors 

 VQ_yV2vVoj. = the characteristic vectors 



The reconstruction of one of the algae curves is shovm in Figure 4 



31-8 



