What are eigenvalues and eigenvectors, and how are they used in Principal Component Analysis?
In: Mathematics
If I remember right, an eigenvector is a vector that is immune to a matrix.
First, you have to think of a matrix as instructions for a transformation. A matrix can tell you to take your space (be it a number line, a cartesian plane, or any other n-dimensional space) and rotate it, squish it, make it wobbly, etc.
When you apply this transformation, any point in your original space will become a different point in your new space.
Any vector that looks the same in the new space as it did in the original space, as in any vector that is not affected by the transformation of a matrix, is an eigenvector of that matrix.
For example if a matrix tells you to stretch a cartesian plane horizontally, such that the horizontal unit vector becomes twice as long, then any vertical vector is an eigenvector of that matrix, because it has no horizontal component and thus is not changed by the transformation.
I’m afraid I don’t know much about the inner workings of PCA.
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