Eigenvalues and eigenvectors

This section provides details on the construction and manipulation of these objects, including matrix facilities that are different from typical element-wise operations.

Matrices

The function eigen(Sm) calculates the eigenvalues and eigenvectors of a symmetric matrix Sm. The result of this function is a list of two components named values and vectors. The assignment

> ev <- eigen(Sm)

will assign this list to ev. Then ev$val is the vector of eigenvalues of Sm and ev$vec is the matrix of corresponding eigenvectors. Had we only needed the eigenvalues we could have used the assignment:

> evals <- eigen(Sm)$values

evals now holds the vector of eigenvalues and the second component is discarded. If the expression

> eigen(Sm)

is used by itself as a command the two components are printed, with their names. For large matrices it is better to avoid computing the eigenvectors if they are not needed by using the expression

> evals <- eigen(Sm, only.values = TRUE)$values

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