- #1
Nusc
- 760
- 2
Homework Statement
If S is a lower triangular matrix (n by n), S^n is the zero matrix.
Homework Equations
The Attempt at a Solution
S =
0 0 0 0 ... 0
1 0 0 0 ... 0
0 1 0 0 ... 0
0 0 1 0 ... 0
...
0 0 0 0 .1.0
S^2 =
0 0 0 0 ... 0
0 0 0 0 ... 0
1 0 0 0 ... 0
0 1 0 0 ... 0
...
0 0 0 0 1.. 0
How do I show this using induction?