Abstract Linear Algebra II
An eigenvector is a non-zero vector that changes only by a scalar factor when a linear transformation is applied to it. This concept is crucial in understanding how linear operators behave, as eigenvectors correspond to specific directions in which these operators stretch or compress space. They are closely related to eigenvalues, which provide the scaling factor associated with each eigenvector, and they play a vital role in diagonalization, allowing matrices to be expressed in simpler forms that reveal their underlying structure.
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