The discussion revolves around expressing the eigenvector of the matrix \sigmax with a +1 eigenvalue as a linear combination of the eigenvectors of another matrix, denoted as M. Participants are exploring the implications of this task within the context of linear algebra and eigenvalues.
The discussion is ongoing, with some participants providing guidance on how to set up the linear combination, while others are seeking clarification on the definition of matrix M and its relevance to the problem.
There is a lack of information regarding the matrix M, which is essential for the discussion on linear combinations of its eigenvectors. This uncertainty is influencing the direction of the conversation.
Okay, that's [itex]\sigma[/itex]. What is M? we can't write something "as a linear combination of the eigenvectors of M without knowing what M is!JordanGo said:Homework Statement
Write the eigenvector of [itex]\sigma[/itex]x with +1 eigenvalue as a linear combination of the eigenvectors of M.
Homework Equations
[itex]\sigma[/itex]x = (0,1),(1,0) (these are the columns)
The Attempt at a Solution
... Don't know what to do. Can someone show me how to do this using arbitrary eigenvectors, say (a,b) and (c,d)?