Finding out eigen-values and eigen-vectors of matrices.

What defines an eigenvector?
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The eigenvalue represents:
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Eigenvalues are found by solving:
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If Av = λv, then v is:
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Eigenvalues can be:
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Eigenvectors must be:
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Eigenvalues help identify:
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In which field are eigenvalues widely used?
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A matrix with distinct eigenvalues has eigenvectors that are usually:
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Eigenvector direction under transformation:
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