Category:Matrix Exponential

This category contains results about the matrix exponential.

Let $\mathbf A$ be a constant square matrix of order $n$.

The matrix exponential of $\mathbf A$, denoted $e^{t \mathbf A}$ or $e^{\mathbf A t}$, is defined as the unique solution to the initial value problem:

$(1): \quad \map {\dfrac \d {\d t} } X = \mathbf A X$

$(2): \quad \map X {\mathbf 0_n} = \mathbf I_n$

where:

$\mathbf I_n$ is the unit matrix of order $n$

$X$ is an order $n$ square matrix which is a function of the real variable $t$

$\mathbf 0_n$ is the zero matrix of order $n$

$\map {\dfrac \d {\d t} } X$ is the derivative of $X$ with respect to $t$.