Several matrix inverse properties

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SUMMARY

The discussion centers on computing the inverse of the product of matrices, specifically (VΔYT)-1, where V is an orthogonal matrix, Δ is diagonal, and Y is nonsingular. The key property utilized is that the inverse of a product of matrices follows the rule (AB)-1 = B-1A-1. The structure of the matrices, such as being orthogonal or nonsingular, does not affect the ability to compute the inverse as long as the dimensions are compatible.

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pob1212
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Hi,

I'm specifically trying to compute (VΔYT)-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
 
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[tex](ABC)^{-1}=(A(BC))^{-1}=(BC)^{-1}A^{-1}=C^{-1}B^{-1}A^{-1}[/tex]

Was that what you were looking for?
 
exactly what I was looking for. Thanks
 

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