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Re: Multiplying matrices

by moritz (Cardinal)
on Mar 10, 2014 at 10:28 UTC ( #1077669=note: print w/ replies, xml ) Need Help??

in reply to Multiplying matrices

Hi Monks.. I am trying to multiply matrices but i want someway to calculate the matrix to the power of x

If your matrices are square, you can decompose your matrix into a product of the form M = U * D * U^T where U is a unitary matrix, U^T is its transposition, and D is a diagonal matrix. Calculating M^x then becomes M^x = U * D^x * U^T, and since D is diagonal calculating the xth power is the same as taking each component to the xth power.

How does the magical decomposition work? My linear algebra fu is a bit rusty, but Matrix decomposition says the singular value decomposition (SVD) can help.

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