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What is an eigenvector?

MIT 18.06 Linear Algebra, Spring 2010
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well, an eigenvector is a non-zero vector that when multiplied with the matrix remain proportional to the original vector, that is, the eigenvector only changes magnitude and does not change direction
If you think of matrix multiplication as moving vectors around, an eigenvector is one that just gets longer or shorter but doesn't change direction.

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your mom is an eigenvector
the concept of shortening or stretching an eigenvector is misleading since it's not the conventional vector space we are dealing with here, rather it's an abstract vector space . well if you want to see the physics behind it is the ensemble of basis which constitutes an experimental system whom we perturb with a physically realizable operator (hermittion) and then we get an observation which is real...i would like to hear back from you on this to know your further queries on this.
the concept of shortening or stretching an eigenvector is misleading since it's not the conventional vector space we are dealing with here, rather it's an abstract vector space . well if you want to see the physics behind it is the ensemble of basis which constitutes an experimental system whom we perturb with a physically realizable operator (hermittion) and then we get an observation which is real...i would like to hear back from you on this to know your further queries on this.

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