linalg(deprecated)/exponential - Help

linalg(deprecated)

 exponential
 matrix exponential

 Calling Sequence exponential(A) exponential(A, t)

Parameters

 A - square matrix t - (optional) scalar parameter of type name

Description

 • Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[MatrixExponential], instead.
 - For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
 • The matrix exponential, ${ⅇ}^{At}$, is a matrix with the same shape as A and is defined as follows: ${ⅇ}^{At}=I+At+\frac{1}{2}!{A}^{2}{t}^{2}+...$ where I is the identity matrix.
 • If the second parameter is not given, then the first indeterminate (if any) in the matrix is removed and used as a parameter.
 • The exponential function can only return a symbolic answer if the eigenvalues of A can be found. To get a floating-point approximation, use at least one floating-point entry in A.
 • The command with(linalg,exponential) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[MatrixExponential], instead.

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\mathrm{array}\left(\left[\left[t,0,0\right],\left[0,t,0\right],\left[0,0,t\right]\right]\right)$
 ${A}{≔}\left[\begin{array}{ccc}{t}& {0}& {0}\\ {0}& {t}& {0}\\ {0}& {0}& {t}\end{array}\right]$ (1)
 > $\mathrm{exponential}\left(A\right)$
 $\left[\begin{array}{ccc}{{ⅇ}}^{{t}}& {0}& {0}\\ {0}& {{ⅇ}}^{{t}}& {0}\\ {0}& {0}& {{ⅇ}}^{{t}}\end{array}\right]$ (2)
 > $B≔\mathrm{array}\left(\left[\left[-13,-10\right],\left[21,16\right]\right]\right)$
 ${B}{≔}\left[\begin{array}{cc}{-13}& {-10}\\ {21}& {16}\end{array}\right]$ (3)
 > $\mathrm{exponential}\left(B,t\right)$
 $\left[\begin{array}{cc}{15}{}{{ⅇ}}^{{t}}{-}{14}{}{{ⅇ}}^{{2}{}{t}}& {-}{10}{}{{ⅇ}}^{{2}{}{t}}{+}{10}{}{{ⅇ}}^{{t}}\\ {21}{}{{ⅇ}}^{{2}{}{t}}{-}{21}{}{{ⅇ}}^{{t}}& {-}{14}{}{{ⅇ}}^{{t}}{+}{15}{}{{ⅇ}}^{{2}{}{t}}\end{array}\right]$ (4)