eigenvector

When an matrix is applied (multiplied) to one of its corresponding eigenvector the eigenvector is only stretched or flipped.

______ Original post / detailed-reaction: > First, every point on the same line as an eigenvector is another eigenvector.

The eigenvalue is the amount the eigenvector is scaled up or down when going through the matrix.

This satisfies the definition of eigenvector and the corresponding diagonal entry of A is the eigenvalue.

The solution to this hedging problem turns out to be the eigenvector of a CDS/exposure matrix, which is kind of fun.

And a principal Eigenvector or two buried in there in some supporting role.

It's a lot less sexy than eigenvector centrality, but I think it would have the intended effect.

And the Gaussian distribution is an eigenvector of the Fourier transform.

True, but it doesn't supply the analytical tools so that you can find the correct A to produce an eigenvector without iteration to reduce error.

At some point in my college Linear Algebra class I realized that the exponential function is an eigenvector of the derivative operator.

I have to admit I hated the term Eigenvector for two semesters of college and it nearly caused me to drop mathematics altogether.

Why do I need to know tomorrow what an ‘principal eigenvector’ is?

Now I can neatly imagine why the eigenvector is orthogonal/perpendicular to the "direction" of the transformation.

In other words, an "eigenvector" is a vector from (0, 0) to any point in an eigenspace.

Let's say that an "eigenvector" is any vector for which our transformation is a scaling.

In these examples two exist, labeled, S1 and S2." "Eigenspaces show where there is 'stability' from repeated applications of the eigenvector.