Linear algebra talks about types of functions called "transformations". In that context, an eigenvector is a vector—different from the null vector—which does not change direction after the transformation (except if the transformation turns the vector to the opposite direction). The vector may change its length, or become zero ("null"). The eigenvalue is the value of the vector's change in length, and is typically denoted by the symbol formula_1. The word "eigen" is a German word, which means "own" or "typical".
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