What is the term for a nonzero vector that only changes by a scalar factor when a linear transformation is applied to it?
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Eigenvector
The term 'eigen' comes from the German word for 'own' or 'characteristic,' highlighting how these vectors represent the fundamental directions of a linear transformation. While most vectors change direction when multiplied by a matrix, eigenvectors simply scale, making them crucial for analyzing stability in everything from bridge design to quantum mechanics.
Also asked as:
- In linear algebra, what is a non-zero vector that, after a transformation, is simply a scaled version of itself?