Eigenvalues of a symmetric 3 × 3 matrix

Authors:
Oliver K. Smith
Affiliations:
Space Technology Lab, Los Angeles, CA
Venue:
Communications of the ACM
Year:
1961

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Abstract

Recently, in order to find the principal moments of inertia of a large number of rigid bodies, it was necessary to compute the eigenvalues of many real, symmetric 3 × 3 matrices. The available eigenvalue subroutines seemed rather heavy weapons to turn upon this little problem, so an explicit solution was developed. The resulting expressions are remarkably simple and neat, hence this note.