At KMP we use several eigenvalue techniques and will show the implementation for eigenvalue problems of real
symmetric matrices.
By definition, an ndimensional vector x is called an eigenvector of a square matrix A if
and only if satisfies the linear equation,
Here λ is a scalar, and is refered to as an eigenvalue corresponding to x. The above
equation is usually called the eigenvalue equation.
Most vectors x will not satisfy the eigenvalue equation. A typical vector x
changes direction when acted on by a matrix A, so that Ax is not a
multiple of x. This means that only certain special vectors x are
eigenvectors, and only certain special scalars λ are eigenvalues.
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