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5 cards from this section. Quick, good the night before a test.
What does an eigenvector represent in the context of linear transformations?
Think about how the transformation affects the direction of the vector.
If the eigenvalue is -1, what do we say about the eigenvector?
Consider what happens to a vector when it is transformed by a negative scale.
What does an eigenvector represent in a linear transformation?
Consider what direction remains unchanged under transformation.
If an eigenvalue is greater than 1, what happens to the corresponding eigenvector?
Publicly relate stretch to scale factors.
Consider a rod modeled with eigenvalues that indicate how it reacts to temperature fluctuations. Discuss how eigenvalues could affect its properties.
Think about how forces can impact state changes in materials.
Analyze a scenario in earthquake engineering where understanding eigenvectors would change design approaches. How do stiffness matrices integrate this knowledge?
Examine past structures' failures for insights.
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