[Math] Exponential of matrix, taylor series

linear algebramatrices

Compute $ exp(X) $for $X=$\begin{bmatrix}t&0\\0&s\end{bmatrix}, \begin{bmatrix}0&t\\-t&0\end{bmatrix} $ and $\begin{bmatrix}0&t\\t&0\end{bmatrix}

The first part of the question I calculated the Taylor series at 0 of $sinh(t), cosh(t), sin(t)$ and $cos(t)$ at $t=0$ so I think I may need to use some of this information for the question. For example I know that $exp(x)=sinh(x)+cosh(x)$

Any help would be much appreciated

Best Answer

Since the first matrix you are dealing with is diagonal, it would be easier to use the formula $exp(X) = \sum_{n=0}^{\infty}\frac{X^n}{n!}$

The diagonal entries will be to the power of n in this sum. Hope this helps.

Related Question