- #1
circa415
- 20
- 0
What exactly is the relationship between the trace/determinant of two matrices with regards to similarity. I always thought that if the trace was the same, then there is a possibility that the matrices are similar and if the determinant was the same, then the matrices are similar. On a recent exam we were given three matrices
A
1 0 1
2 3 5
0 2 -6
B
-4 3 4
0 1 2
0 0 1
C
0 0 2
0 4 1
3 5 -2
One of these matrices is similar to A.
I found det(a) = det (c) but trace (a) is not equal to trace (c). Det(B) is not equal to det (a) but trace (a) = Trace (b). Do I have my facts wrong?
A
1 0 1
2 3 5
0 2 -6
B
-4 3 4
0 1 2
0 0 1
C
0 0 2
0 4 1
3 5 -2
One of these matrices is similar to A.
I found det(a) = det (c) but trace (a) is not equal to trace (c). Det(B) is not equal to det (a) but trace (a) = Trace (b). Do I have my facts wrong?