The basic assumption underlying the linear mixture model
is that the different classes present in a pixel contribute
independently to its reflectance. Therefore, the
reflectance of a pixel at a particular frequency is the sum
of the reflectances of the components of that pixel,
at that frequency [],[]. If the vector 
were to
be estimated from a single intensity value of the pixel,
the problem would be highly underdetermined. However,
typically, the same region is imaged at several different
frequencies (spectral bands), leading to multispectral
observations for each pixel. To formalize this;
Consider a single pixel and let the vector of proportions
of the different cover classes be 
.
where c is
the number of classes and 
denotes the
proportion (a fraction between 0.0 and 1.0) of class `i' within that pixel.
The multispectral observations for that pixel are denoted by
where n is
the number of bands over which the observations are made
and 
denotes the spectral response in band `j' for
that pixel.
The linear relation follows as :
where 
denotes the spectral response that a
pure pixel (proportion of 1.0) of cover class `j' would
produce in spectral band `i'. 
denotes the error
between the linear combination of the fractions and the
actual observation.
In matrix notation,
The matrix 
is conventionally known as the "endmember
matrix". In addition to these mixing equations, we have the
constraint that in any
given pixel, the proportions must sum to one; i.e.,
where 
is a 
vector
containing all ones.