The eigenvalue is the value of the vector's change in length, and is typically denoted by the symbol. . The word "eigen" is a German word, which means "own" or "typical".

What is an eigenvalue in simple terms?

: a scalar associated with a given linear transformation of a vector space and having the property that there is some nonzero vector which when multiplied by the scalar is equal to the vector obtained by letting the transformation operate on the vector especially : a root of the characteristic equation of a matrix.

How do you explain eigenvalues?

An eigenvalue is a number, telling you how much variance there is in the data in that direction, in the example above the eigenvalue is a number telling us how spread out the data is on the line. The eigenvector with the highest eigenvalue is therefore the principal component.