Exponentiating $2\times2$ and $3\times3$ Matrices Done Right

Details Exponentiating $2\times2$ and $3\times3$ Matrices Done Right Exponentiating $2\times2$ and $3\times3$ Matrices Done Right

2007-12-17

arxiv.org/abs/0712.2632v1

Mathematics

History and Overview

17 pages

Scientific paper

We derive explicit formulas for calculating $e^A$, $\cosh{A}$, $\sinh{A}, \cos{A}$ and $\sin{A}$ for a given $2\times2$ matrix $A$. We also derive explicit formulas for $e^A$ for a given $3\times3$ matrix $A$. These formulas are expressed exclusively in terms of the characteristic roots of $A$ and involve neither the eigenvectors of $A$, nor the transition matrix associated with a particular canonical basis. We believe that our method has advantages (especially if applied by non-mathematicians or students) over the more conventional methods based on the choice of canonical bases. We support this point with several examples for solving first order linear systems of ordinary differential equations with constant coefficients.

Affiliated with

Also associated with

No associations

Rating

Exponentiating $2\times2$ and $3\times3$ Matrices Done Right does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exponentiating $2\times2$ and $3\times3$ Matrices Done Right, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exponentiating $2\times2$ and $3\times3$ Matrices Done Right will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-115783