Hey guys

I have this question i've been trying to solve for too long:

 

Let A be an nxn matrix, rankA=1 , and n>1 .

Prove that A is either nilpotent or diagonalizable.

 

I have no clue how to even get started with that... though i attempted too much...

 

Anyone can help?

 

Thanks a lot

Start with some definitions. What is a nilpotent matrix, and a diagonalizable matrix? What are some key characteristics of such matrices? Finally, what does rank mean?

 

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yeah i know... and i tried, and i failed.. that's why i'm asking.

anyway, let's see...

a matrix is said to be nilpotent if there is some 'k' such that A^k = 0.

diagonalizable matrix is such one that is similar to a diagonal matrix.

and i can't get anything helpful from the rank 1 thing...

What about eigenvalues?