Category:Matrix Exponential

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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:

$(1): \quad \map {\dfrac \d {\d t} } X = \mathbf A X$
$(2): \quad \map X {\mathbf 0_n} = \mathbf I_n$


$\mathbf I_n$ 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 $t$.