Several matrix inverse properties

[pob1212]

Hi,

I'm specifically trying to compute (VΔY^T)^-1, where V is nxn and orthogonal, Δ is diagonal, and Y is nonsingular.

In general we have (AB)^-1 = B^-1A^-1

But how do we do this in general for many matrices? Is there a method, and as long as the matrix dimensions agreed, does the structure (i.e. orthogonal, nonsingular, SPD, etc) matter when computing the inverse of multiple matrices?

I can't find this anywhere on the internet.

Thanks

 

[micromass]

$$(ABC)^{-1}=(A(BC))^{-1}=(BC)^{-1}A^{-1}=C^{-1}B^{-1}A^{-1}$$

Was that what you were looking for?

 

[pob1212]

exactly what I was looking for. Thanks