A 1-PAM mutation matrix describes an amount of evolution which
will change, on the average, 1% of the amino acids.
In mathematical terms this is expressed as a matrix *M* such that

The diagonal elements of

If we have a probability or frequency vector *p*, the product
*Mp* gives the probability vector or the expected frequency
of *p* after an evolution equivalent to 1-PAM unit.
Or, if we start with amino acid *i* (a probability vector
which contains a 1 in position *i* and 0s in all others)
*M*_{*i} (the *i*^{th} column of *M*) is the corresponding
probability vector after one unit of random evolution.
Similarly, after *k* units of evolution (what is
called *k*-PAM evolution) a frequency vector *p* will be
changed into the frequency vector *M*^{k} *p*.
Notice that chronological time is not linearly dependent on PAM distance.
Evolution rates may be very different for different species
and different proteins.