I have the following $ 8 times $ 8 matrix

```
{{1/3 (2 c(0,0)-c(1,0)-c(2,0)),(c(1,0)-c(2,0))/Sqrt(3),0,1/3 (-1+c(0,0)+c(0,1)+3 c(0,2)+c(1,0)+c(1,1)+c(2,0)+c(2,1)),-((-1+c(0,0)+c(0,1)+c(0,2)+c(1,0)+c(1,1)+2 c(1,2)+c(2,0)+c(2,1))/Sqrt(3)),1/3 (2 c(0,1)-c(1,1)-c(2,1)),(c(1,1)-c(2,1))/Sqrt(3),0},{(c(1,0)-c(2,0))/Sqrt(3),1/3 (-2 c(0,0)+c(1,0)+c(2,0)),0,(-1+c(0,0)+c(0,1)+c(0,2)+c(1,0)+c(1,1)+2 c(1,2)+c(2,0)+c(2,1))/Sqrt(3),1/3 (-1+c(0,0)+c(0,1)+3 c(0,2)+c(1,0)+c(1,1)+c(2,0)+c(2,1)),(c(1,1)-c(2,1))/Sqrt(3),1/3 (-2 c(0,1)+c(1,1)+c(2,1)),0},{0,0,-(1/3)+c(0,0)+c(1,0)+c(2,0),0,0,0,0,(-1+c(0,0)+2 c(0,1)+c(1,0)+2 c(1,1)+c(2,0)+2 c(2,1))/Sqrt(3)},{1/3 (2 c(0,1)-c(1,1)-c(2,1)),(c(1,1)-c(2,1))/Sqrt(3),0,1/3 (2 c(0,0)-c(1,0)-c(2,0)),(-c(1,0)+c(2,0))/Sqrt(3),1/3 (-1+c(0,0)+c(0,1)+3 c(0,2)+c(1,0)+c(1,1)+c(2,0)+c(2,1)),(-1+c(0,0)+c(0,1)+c(0,2)+c(1,0)+c(1,1)+2 c(1,2)+c(2,0)+c(2,1))/Sqrt(3),0},{(-c(1,1)+c(2,1))/Sqrt(3),1/3 (2 c(0,1)-c(1,1)-c(2,1)),0,(-c(1,0)+c(2,0))/Sqrt(3),1/3 (-2 c(0,0)+c(1,0)+c(2,0)),-((-1+c(0,0)+c(0,1)+c(0,2)+c(1,0)+c(1,1)+2 c(1,2)+c(2,0)+c(2,1))/Sqrt(3)),1/3 (-1+c(0,0)+c(0,1)+3 c(0,2)+c(1,0)+c(1,1)+c(2,0)+c(2,1)),0},{1/3 (-1+c(0,0)+c(0,1)+3 c(0,2)+c(1,0)+c(1,1)+c(2,0)+c(2,1)),(-1+c(0,0)+c(0,1)+c(0,2)+c(1,0)+c(1,1)+2 c(1,2)+c(2,0)+c(2,1))/Sqrt(3),0,1/3 (2 c(0,1)-c(1,1)-c(2,1)),(-c(1,1)+c(2,1))/Sqrt(3),1/3 (2 c(0,0)-c(1,0)-c(2,0)),(c(1,0)-c(2,0))/Sqrt(3),0},{(-1+c(0,0)+c(0,1)+c(0,2)+c(1,0)+c(1,1)+2 c(1,2)+c(2,0)+c(2,1))/Sqrt(3),1/3 (1-c(0,0)-c(0,1)-3 c(0,2)-c(1,0)-c(1,1)-c(2,0)-c(2,1)),0,(c(1,1)-c(2,1))/Sqrt(3),1/3 (2 c(0,1)-c(1,1)-c(2,1)),(c(1,0)-c(2,0))/Sqrt(3),1/3 (-2 c(0,0)+c(1,0)+c(2,0)),0},{0,0,-((-1+c(0,0)+2 c(0,1)+c(1,0)+2 c(1,1)+c(2,0)+2 c(2,1))/Sqrt(3)),0,0,0,0,-(1/3)+c(0,0)+c(1,0)+c(2,0)}}
```

It has forty non-zero entries, some of which are duplicates and some of which are negatives of others. I want to map the entry (1,1) to t (1) and the following entries to t (i) or -t (i) – taking into account identities and "negative identities" – so that the length of the array of t is minimum.

In other words, what is the minimum number of t (i) I need to recode the original $ 8 times $ 8 matrix, and what mapping does it achieve?

My ultimate goal is to get the product and the sum of the singular values of the matrix, and I hope that a succinct recoding of it could facilitate such a task.