Abstract: A compiler and/or a compilation method is used to change or compile a plurality of instructions in memory from a form which is better understood by a human user to a form which is readily executed by a microprocessor. In doing this compilation, execution optimization is usually performed. A more efficient job of optimization (and therefore improved software performance) is achieved by correctly finding/identifying induction variables in code loops which may be used in the compiler's optimization routines. Induction variable properties can be found by constructing and analyzing an integer transfer matrix wherein the values of variables at the beginning of one execution of the loop are related functionally to the values of variables at the end of the one execution of the loop. This matrix can be effectively processed using eigenvalue processing using integer unimodular matrices to determine induction variable properties which were previously missed by prior methods, thereby improving performance.