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what is the difference between right and left eigenvector?

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Sarah A
Sarah A on 9 Aug 2018
Edited: Stephen Cobeldick on 10 Aug 2018
Hello,
I read here: https://www.mathworks.com/help/matlab/ref/eig.html that there are two types of eigenvectors, I googled this but with no results. So can any one tell me what is the difference ?

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Answers (1)

Stephen Cobeldick
Stephen Cobeldick on 10 Aug 2018
Edited: Stephen Cobeldick on 10 Aug 2018
etc.
The difference is simply which side they occur on during the multiplication with the matrix A used in their definition.
A right eigenvector as a column vector X_R satisfies:
A * X_R = lambda_R * X_R
A left eigenvector as a row vector X_L satisfies:
X_L * A = lambda_L * X_L
From wikipedia: "Many disciplines traditionally represent vectors as matrices with a single column rather than as matrices with a single row. For that reason, the word 'eigenvector' in the context of matrices almost always refers to a right eigenvector".

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