MatrixExp
MatrixExp[m]
gives the matrix exponential of m.
MatrixExp[m,v]
gives the matrix exponential of m applied to the vector v.
Details and Options

- MatrixExp[m] effectively evaluates the power series for the exponential function, with ordinary powers replaced by matrix powers.
- MatrixExp works only on square matrices.
- In MatrixExp[m,v] the matrix m can be a SparseArray object.
Examples
open allclose allScope (22)
Basic Uses (6)
Exponentiate a machine-precision matrix:
Exponentiate a complex matrix:
Compute the exponential of an exact matrix:
The exponential of an arbitrary-precision matrix:
Exponential of a symbolic matrix:
Computing the exponential of large machine-precision matrices is efficient:
Directly applying the exponential to a single vector is even more efficient:
Special Matrices (5)
The exponential of a sparse matrix is returned as a normal matrix:
Directly apply the matrix exponential of a sparse matrix to a sparse vector:
Compute the exponential of a structured array:
Exponentiate IdentityMatrix:
More generally, the exponential of any diagonal matrix is the exponential of its diagonal elements:
Exponentiate HilbertMatrix:
Scratch (11)
Find the matrix exponential of a MachinePrecision matrix:
Use matrix exponential for a complex matrix:
Use matrix exponential for an exact matrix:
Use matrix exponential for an arbitrary-precision matrix:
Use matrix exponential for a HilbertMatrix:
Use matrix exponential for an IdentityMatrix:
Matrix exponential of a sparse matrix:
Matrix exponential of a structured matrix:
Matrix exponential of a non-square matrix:
The exponential of a symbolic matrix:
Find the matrix exponential of a large matrix applied to a vector:
Applications (2)
A system of first-order linear differential equations:
Write the system in the form with
:
The matrix exponential gives the basis for the general solution:
The matrix exponential applied to a vector gives a particular solution:
The matrix s approximates the second derivative periodic on on the grid x:
A vector representing a soliton on the grid x:
Propagate the solution of using a splitting
:
Plot the solution and 10 times the error from the solution of the cubic Schrödinger equation:
Properties & Relations (4)
Possible Issues (1)
Neat Examples (1)
Text
Wolfram Research (1991), MatrixExp, Wolfram Language function, https://reference.wolfram.com/language/ref/MatrixExp.html (updated 2007).
BibTeX
BibLaTeX
CMS
Wolfram Language. 1991. "MatrixExp." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/MatrixExp.html.
APA
Wolfram Language. (1991). MatrixExp. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MatrixExp.html