Matrix exponential

In mathematics, particularly in the study of Lie groups and Lie algebras, the matrix exponential is the function on square matrices A defined by

This concept has applications to systems of linear differential equations.

In some cases we have

but when A and B commute with each other, the familiar identity holds.

If A is a skew-symmetric matrix then e^A is an orthogonal matrix.

If a matrix is diagonal

then its exponential can be obtained by just exponentiating every entry:

This also allows to exponentiate diagonalizable matrices. If A = U⁻¹DU and D is diagonal, then e^A = U⁻¹e^DU.

This article is a stub. You can help Wikipedia by expanding it .