The basic equation is Ax = λx The number or scalar value “ λ” is an eigenvalue of A. In Mathematics, an eigenvector corresponds to the real non zero
Eigenvalue Equations The time independent Schrödinger Equation is an example of an Eigenvalue equation. The Hamiltonian operates on the eigenfunction , giving a constant the eigenvalue
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In that case the eigenvector is the direction that doesn't change direction ! And the eigenvalue is the scale of the stretch: 1 means no change, 2 means doubling in length, −1 means pointing backwards along the eigenvalue's direction. etc.
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referred to as the eigenvalue equation or eigenequation. In general, λ may be any scalar. For example, λ may be negative, in which case the eigenvector reverses
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