There are a set of firstnames: david, anton, fred, jim, barry which are numbered 1 (david) to 5 (barry) and a set of surnames: barber, ilsung, fox, chain, fitzwilliam, quinceadams, grafvonunterhosen, which are numbered 1 (barber) to 7 (grafvonunterhosen). A string is generated by first randomly sampling a character from a to z

To diagonalize an nxn matrix a means to find an invertible matrix p and a diagonal matrix d such that a pdp d p ap or [1 3 dh epap 3 let a=-3 -5 -3 3 3 1 step 1: find the eigenvalues of matrix a "2's" step 2: find the corresponding eigenvectors of a step 3: createp from eigenvectors in step 2 step 4 create d with matching eigenvalues.