Q:

Does this Dirac Delta Exist in multivariate form?

Is there a multi-variate equivalent to the Dirac-Delta?
Like $\delta (X - A)$ that is infinity whenever $X=A$ and zero everywhere else and X, A positive-definite n by n squares so that I could integrate this over the Haar measure say as in
\begin{eqnarray}
\int_{X>0} \delta (X-A)=I_n
\end{eqnarray}
?
Thanks!

A:

Yes, you can use the identity 
\begin{eqnarray}
\delta(X-A) = \int_{-\infty}^\infty \frac{e^{ik(X-A)}}{2 \pi}dk
\end{eqnarray}. 
Then you can compute the Matrix exponential. 

