On the relations between eigenvalues and eigenvectors for matrices resulting from pre and post multiplication by the transpose

Law, V. J.; Fariss, R. H.

doi:10.1090/S0025-5718-1968-0238869-6

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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On the relations between eigenvalues and eigenvectors for matrices resulting from pre and post multiplication by the transpose
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by V. J. Law and R. H. Fariss PDF

Math. Comp. 22 (1968), 867-868 Request permission

Abstract:

Relationships between the eigenproblem associated with the matrices ${A^T}A$ and $A{A^T}$ are derived. If the larger problem is solved first, then the eigenvalues and eigenvectors associated with the smaller problem may easily be computed from the derived relationships.

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