The "academic trace" of the performance matrix: a mathematical synthesis of the h‐index and the integrated impact indicator (I3)

The h-index provides us with 9 natural classes which can be written as a matrix of 3 vectors. The 3 vectors are: X = (X1, X2, X3) and indicates publication distribution in the h-core, the h-tail, and the uncited ones, respectively; Y = (Y1, Y2, Y3) denotes 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 9 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 2 journal sets, 2 universities, and ourselves as 2 individual authors.