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. For a symmetric 2x2 matrix (like the covariance matrices built in this lesson), what special property do its eigenvectors have?
A symmetric 2x2 matrix always has two perpendicular (orthogonal) eigenvectors with real eigenvalues.
. In the covariance matrix built from a blob's central moments, what do the eigenvectors represent geometrically?
Diagonalizing the covariance matrix rotates into the frame where the blob's spread in x and y no longer mixes -- exactly its major/minor axes.
. What does an eccentricity close to 0 indicate about a shape?
Eccentricity ranges from 0 (a circle) to nearly 1 (a very thin, elongated shape).
. This lesson notes that eigendecomposing a covariance matrix of general (not necessarily image) data is known as what technique?
PCA is the same diagonalization operation applied to a covariance matrix of general data, ranking eigenvectors by eigenvalue as principal components.