Simple Linear Algebra problem that's confusing me.

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Yingquan Li
Yingquan Li . 2012년 4월 25일
I'm stuck for the longest time on this problem: Find a row vector l such that lA = l, with A = [.2 .8; .7 .3]. This is somehow related to eigenvalues, is there such thing as a row eigenvector? thanks - Yingquan
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Richard Brown
Richard Brown 2012년 4월 26일
a "row" eigenvector is usually called a left eigenvector

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답변 (1개)

Wayne King
Wayne King 2012년 4월 25일
I don't want to just give you the answer, but think of it this way
1.) Think of the typical eigenvalue problem, I'll use B as the matrix
Bx = \lambda x
2.) if 1 were an eigenvalue of B with some corresponding eigenvector x, then
Bx = x
3.) Now what if you transposed both sides of the above equation and let B'=A (where ' is the transpose)
Now do you see?
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Richard Brown
Richard Brown 2012년 4월 26일
don't forget the rule about transposing products ...

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