proof of Taylor’s formula for matrix functions
Let be a polynomial and suppose and are squared matrices of the same size, then where .
Since is a polynomial, we can apply the Taylor expansion:
where . Now let and .
The Taylor expansion can be checked as follows: let for coefficients (note that this coefficients can be taken from the space of square matrices defined over a field). We define the formal derivative of this polynomial as and we define .
Then and we have . Now consider
since . ∎
|Title||proof of Taylor’s formula for matrix functions|
|Date of creation||2013-03-22 17:57:04|
|Last modified on||2013-03-22 17:57:04|
|Last modified by||joen235 (18354)|