  The h-index provides us with nine natural classes which can be written as a
matrix of three vectors. The three vectors are: X=(X1, X2, X3) indicate
publication distribution in the h-core, the h-tail, and the uncited ones,
respectively; Y=(Y1, Y2, Y3) denote the citation distribution of the h-core,
the h-tail and the so-called "excess" citations (above the h-threshold),
respectively; and Z=(Z1, Z2, Z3)= (Y1-X1, Y2-X2, Y3-X3). The matrix V=(X,Y,Z)T
constructs a measure of academic performance, in which the nine numbers can all
be provided with meanings in different dimensions. The "academic trace" tr(V)
of this matrix follows naturally, and contributes a unique indicator for total
academic achievements by summarizing and weighting the accumulation of
publications and citations. This measure can also be used to combine the
advantages of the h-index and the Integrated Impact Indicator (I3) into a
single number with a meaningful interpretation of the values. We illustrate the
use of tr(V) for the cases of two journal sets, two universities, and ourselves
as two individual authors.
