Null matrix can be an idempotent matrix?

1. Jan 2, 2015

gianeshwar

Friends!
Is there anything wrong in the statement"A null matrix is idempotent".

2. Jan 2, 2015

Staff: Mentor

What do you think? How is the term "idempotent" defined?

3. Jan 2, 2015

gianeshwar

A square equal A. So if A is zero matrix then it satsfies this condition.

4. Jan 2, 2015

Staff: Mentor

Any square zero matrix A is idempotent, since A2 = A. So, in regard to your question in the first post, not all zero matrices are idempotent, since A2 might not be defined. For example,
$$A = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0\end{bmatrix}$$

5. Jan 2, 2015

gianeshwar

Thank You.Doubt had arisen while showing B square not equal to I to be not always true when given B equal I minus A and A is idempotent.

6. Jan 2, 2015

Staff: Mentor

I'm not sure what you're trying to say here. Writing an equation would make it clearer.

Are you saying that B = I - A, and A is idempotent? And you need to show that B2 ≠ I?

If so, that's easy to show -- just expand B2 = (I - A)2.

7. Jan 3, 2015

gianeshwar

I needed to show that( B squarenot equai to I) is not always true.

8. Jan 3, 2015

Staff: Mentor

Like I said in my previous post, this is easy to do.

Also, please take some time to learn how to write proper math notation. To indicate the square of something, at the very least you can write B^2. Better yet, write the exponent as a superscript, like this: B2. The x2 icon in the menu bar can be used to write exponents of all kinds. The $\Sigma$ icon in the menu bar has many math symbols, such as ≠ and ∞ and many others.

9. Jan 4, 2015

gianeshwar

Thank You Mark44 for the valuable help and suggestions!

10. Jan 4, 2015

Staff: Mentor

You're welcome!