Practice question · Multiple choice
PageRank ranks web pages using the principal eigenvector of a link matrix. Why should an eigenvector be the right object for ranking importance?
Hints
- Write down what makes a page important. Notice the definition refers to itself.
- Ask what Av = lambda v says about a vector of page scores.
Show the answer
B. Because importance is defined circularly, which is what an eigenvector is.
Why
The definition is circular by design, a page is important if important pages link to it, and writing that out gives Av = λv. So the circularity that makes it look useless is exactly what an eigenvector resolves. Power iteration is both the proof that it settles and the algorithm at web scale, which is why the same mathematics appears in spectral clustering and recommenders.
Practise Eigenvalues and Eigenvectors
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More questions on Eigenvalues and Eigenvectors
- Sort each statement about eigenvalues and eigenvectors as true or false.
- PageRank computes its scores by multiplying a vector by the link matrix over and over until it stops…
- The diagonal matrix with rows (5, 0) and (0, -1) acts on the plane. Select every TRUE statement.
- An eigenvector keeps its direction under the matrix but may be stretched, shrunk or flipped.