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STEP Support Programme

Invariant Lines and Eigenvectors


I've never learned about invariant lines but I know how to get eigenvectors. I know the difference is just the constant term, so is there any simple way to get invariant lines after getting the eigenvectors/values of a matrix? Thank you.

Is it correct to say that if eigenvalue lamda=1, then the invariant line is just the line with direction of the eigenvector and goes through origin (constant is zero), and if lamda != 1, then invariant line is eigenvector plus an arbitary constant?

I just saw the answer in the support module notes. Sorry!


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University of Cambridge Mathematics Faculty: What do we look for?

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University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

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AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)