Take the 2-minute tour ×
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.

I have a matrix-vector inner product multiplication $G = X D x$ where $D$ is a diagonal matrix. Now let's say I already know $E = Xx$. Is there a method that I can use to change $E$ into $G$ using $D$ without having to calculate $G$ in full?

share|improve this question
add comment

2 Answers

up vote 0 down vote accepted

Merely knowing the vector $E$ and the matrix $D$ doesn't seem to be enough to determine $G$, since $E$ is some vector in the column space of $X$, and $G$ can be more or less any other vector in that column space. I don't see how you can tell what $G$ is without using what the individual columns in $X$ are and how they were combined to obtain $E$.

share|improve this answer
add comment

I love cheap answers because they help in asking good questions. So you have $G=XDX^{-1}E$ How do you intend to use $G$ that this does not satisfy? I don't understand where diagonal comes into this.

share|improve this answer
    
To clarify: I know $E$, but I do not want to use $X$ and $x$ in further calculations if possible. Diagonal may not be relevant, just mentioned it in case it could simplify the problem. –  Projectile Fish Feb 3 '11 at 6:10
add comment

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.