Without qualification, the term eigenvectors (of a matrix) refers to the column eigenvectors (of a matrix) and can be directly computed with Eigenvectors[]. To get the row eigenvectors, one can invert the transpose of the matrix returned by Eigenvectors[] (or equivalently, the inverse of JordanDecomposition[][[1]]).

This approach is usually fast enough, but sometimes, computing the inverse takes an enormous amount of time compared to just computing the column eigenvectors. This can happen when the column eigenvectors are partially symbolic, or involve Root[].

Is there a better way to compute the row eigenvectors of a matrix? In particular, is there a way to compute the row eigenvectors as fast as the column eigenvectors?

Without qualification, the term eigenvectors (of a matrix) refers to the column eigenvectors (of a matrix) and can be directly computed with Eigenvectors[]. To get the row eigenvectors, one can invert the transpose of the matrix returned by Eigenvectors[] (or equivalently, the inverse of JordanDecomposition[][[1]]).

This approach is usually fast enough, but sometimes, computing the inverse takes an enormous amount of time, compared to just computing the column eigenvectors. This can happen when the column eigenvectors are partially symbolic, or involve Root[].

Is there a better way to compute the row eigenvectors of a matrix? In particular, is there a way to compute the row eigenvectors as fast as the column eigenvectors?

Without qualification, the term eigenvectors (of a matrix) refers to the column eigenvectors (of a matrix) and can be directly computed with Eigenvectors[]. To get the row eigenvectors, one can invert the transpose of the matrix returned by Eigenvectors[] (or equivalently, the inverse of JordanDecomposition[][[1]]).

This approach is usually fast enough, but sometimes computing the inverse takes an enormous amount of time compared to just computing the column eigenvectors. This can happen when the column eigenvectors are partially symbolic or involve Root[].

Is there a better way to compute the row eigenvectors of a matrix? In particular, is there a way to compute the row eigenvectors as fast as the column eigenvectors?

Without qualification, the term eigenvectors (of a matrix) refers to the column eigenvectors (of a matrix) and can be directly computed with Eigenvectors[]. To get the row eigenvectors, one can invert the transpose of the matrix returned by Eigenvectors[] (or equivalently, the inverse of JordanDecomposition[][[1]]).

This approach is usually fast enough, but sometimes, computing the inverse takes an enormous amount of time compared to just computing the column eigenvectors. This can happen when the column eigenvectors are partially symbolic, or involve Root[].

Is there a better way to compute the row eigenvectors of a matrix? In particular, is there a way to compute the row eigenvectors as fast as the column eigenvectors?