gives the matrix exponential of m.
gives the matrix exponential of m applied to the vector v.
Examplesopen allclose all
Basic Examples (3)
Basic Uses (6)
Special Matrices (5)
Verify the solution using DSolveValue:
In quantum mechanics, the energy operator is called the Hamiltonian . Given the Hamiltonian for a spin-1 particle in constant magnetic field in the direction, find the state at time of a particle that is initially in the state representing :
Cross products with respect to fixed three-dimensional vectors can be represented by matrix multiplication, which is useful in studying rotational motion. Construct the antisymmetric matrix representing the linear operator , where is an angular velocity about the axis:
Verify using RotationMatrix:
Properties & Relations (10)
MatrixExp of a real, antisymmetric matrix is orthogonal:
MatrixExp of an antihermitian matrix is unitary:
MatrixExp of a Hermitian matrix is positive-definite:
MatrixExp satisfies :
can be computed from the JordanDecomposition as
Possible Issues (1)
Neat Examples (1)
Wolfram Research (1991), MatrixExp, Wolfram Language function, https://reference.wolfram.com/language/ref/MatrixExp.html (updated 2014).
Wolfram Language. 1991. "MatrixExp." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/MatrixExp.html.
Wolfram Language. (1991). MatrixExp. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MatrixExp.html