This is not as easy as it sounds, but not too bad.  In principle, you just calculate the Nth root of your [T] matrix as you have suggested.  However, you have a matrix [T] to do this with and not a scalar quantity so the manner in which is happens is a little different.  If you have MATLAB, you could experiment with the function funm() to do this.  Alternatively, you could approximate the Nth root with a series, which then you apply to your matrix to calculate the Nth root.

Thanks for the answer sir. A bit more detailed answer will be highly appreciated as i am new to this.

See attached.

Thanks again sir for the prompt and detailed reply. I hope this will solve my purpose.

Sir, I was wondering if we can get exactly the T matrix from the normalized T2 matrix obtained in the pdf ? I need to get the exact T matrix ,  not the normalized form T2 . Thanks in advance.

I do not know.  You may try multiplying [T2] by the Nth root of the norm of [M] and see if it matches [T], but I do not know if that will work.

Thanks for the suggestion. I shall try it out.

Ho ravi !

Did you find a solution for your problem ?

I am in thé dame case : )