Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 0 down vote favorite

I have a binary vector b $\in \{0,1\}^n$ , and C = diag(b) is a $n \times n$ diagonal matrix.

Is there any decomposition or transformation like bx = C , so that we can generalize x ?

share|improve this question
If that is supposed to represent ordinary matrix multiplication, the answer is no, because $\mathbf{b}$ has rank at most $1$, and $\mathbf{C}$ can have any rank up to $n$. If you just are asking whether there is a linear tranformation that sends $\mathbf{b}$ to $\mathbf{C}$, the answer is yes, and it generalizes to sending an arbitrary $n$-tuple to the corresponding diagonal matrix. Could you please clarify what the question is? – Jonas Meyer Feb 8 '11 at 17:49
yes, by x i mean transformation matrices/ vectors, that are required to obtain the diagonal matrix C – user5978 Feb 9 '11 at 9:03

1 Answer

up vote 1 down vote

The way you have defined it, for all $i$ where $b_i=1$, $x$ must have a 1 on the main diagonal and zeros elsewhere. Is this what you mean by "generalize x"?

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.