### Linear Combination

For the Morro Bay TM scene there are 7 spectral bands. Thus each pixel has
7 values. The pixel in row i, column j of the image is a vector:

x(i,j,1) x(i,j,2) x(i,j,3) x(i,j,4) x(i,j,5) x(i,j,6) x(i,j,7)

x(i,j,1) is the value of band 1 in row i, column j, x(i,j,2) is
the value of band 2 in row i, column j, etc.

A linear combination of these values, to calculate the first Principal
Component, would look like:

This multiplication and addition is carried out for each of the picture elements,
pixels, in the image. The Principal Components Analysis
is the calculation of the values of the set of vectors __a__ and then the
multiplication of the image data by them to get the projections of the data
points onto the Principal Components.

Nicholas M. Short, Sr.
email: [email protected]

Dr. Jon W. Robinson ([email protected])