There are two eigenvalues 𝜆=1, that are equal to each other. Thus, shear transformation has only one eigenvector

This statement is wrong right? It’s possible to have two eigenvalues with the same value, and have two different eigenvectors.

There are two eigenvalues 𝜆=1, that are equal to each other. Thus, shear transformation has only one eigenvector

This statement is wrong right? It’s possible to have two eigenvalues with the same value, and have two different eigenvectors.

Hi, thanks for your message!

Yes, this statement is not precise. In fact if v is an eigenvector of a linear transformation T, then a \cdot v is also an eigenvector, for every a \in \mathbb{R}.

Thanks, for noticing it, I will inform our team to fix this statement!

Lucas