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I created a exp function for a matrix, had to first create a pow
function then exp could call that
no problem
so I used a taylor expansion to do the work
so it got me thinking, do vectors and matrices all good with taylor
expansions etc
Rob Beezer
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Feb 27, 2012, 7:46:36 PM2/27/12
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You can form any polynomial of a square matrix, since powers make sense, and then scalar multiples and addition are the most basic operations. This is Subsection EE.PM.
With vectors this would not be so natural, but it is sometimes advantageous to multiply a polynomial of a square matrix times a vector. See the proof of Theorem EMHE.
Rob
Vegan
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Mar 2, 2012, 8:47:53 AM3/2/12
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Thanks, I was considering something along the line of exp(A) where A is a matrix etc
template <typename T> matrix<T> pow(matrix<T> &radix, int signficand) { matrix<T> product = radix; for (int i = 1; i < significand; i++) // Brutal computations product = product * radix; return product; }
template <typename T> matrix<T> exp(matrix<T> &exponent) { matrix<T> sum = 0; // Maclaurin series expansions for (int k = 0; k < 6; k++) { // 6 terms should be enough sum = sum + (pow(exponent, k) / factorial(k)); // Power series } return sum; }