$$B^2=0$$
solve for B

Question

$$B^2=0$$
solve for B

inkyvoyd · Answer

Take the positive and negative square root of both sides.

unklerhaukus · Answer

is there any solution other than the trivial

inkyvoyd · Answer

Solve the problem of the ambiguous expression -0 and +0

inkyvoyd · Answer

You find that both are equivalent.

inkyvoyd · Answer

Resubstitute for confirmation. Tell me what you got, and what you mean by trivial.

unklerhaukus · Answer

well B=0 is the trivial soluton

unklerhaukus · Answer

if B is a number B=0

what if B is a matrix? what are the the solutions?

inkyvoyd · Answer

In that case you probably should
A. Mention that it's a matrix first
B. ask someone like @apoorvk who I think knows how to solve this.

unklerhaukus · Answer

If $$\textbf{B}=\begin{bmatrix} 0 & 1 \ 0 & 0  \end{bmatrix}$$
$$\textbf{B}^2=0$$
does not require B=0

anonymous · Answer

You should study group theory, or introduction to abstract algebra. Here is a source that talks about when B^n = 1, but not about 0 unfortunately: http://www-history.mcs.st-and.ac.uk/~edmund/lnotes/node8.html

unklerhaukus · Answer

one day i will

apoorvk · Answer

Well, yes a null matrix, does not necessarily have to be the product of a matrix and another null matrix. Any matrix when squared can equal a null matrix, if the elements are suit so. More importantly every nilpotent matrix (one whose diagonal elements are 0) satisfies the above condition. Check this link out, should help: http://en.wikipedia.org/wiki/Nilpotent_matrix

anonymous · Answer

ah yes, nilpotent.  key word.

apoorvk · Answer

**elements suit it.