does this mean a matrix is singular?

Printable View

Jan 27th 2010, 09:32 PM
superdude

does this mean a matrix is singular?

If a matrix A $\neq$ 0 and $A^k=0$ where k is a positive integer, does that mean A is singular?
Jan 27th 2010, 10:05 PM
nehme007

A must be singular. Suppose not, then there exists $A^{-1}$ satisfying $AA^{-1}=A^{-1}A = I$ . Then $A^k (A^{-1})^k = I = 0$ , giving a contradiction.
Jan 27th 2010, 11:15 PM
superdude

so the =0 means a matrix full of zeros right?
Jan 28th 2010, 12:42 AM
HallsofIvy

Quote:

Originally Posted by superdude

so the =0 means a matrix full of zeros right?

Yes, that is the 0 matrix.

All times are GMT -8. The time now is 09:18 PM.