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Eigenvalue Problem Solutions

At Keystone Mining Post we use several eigenvalue techniques and will show the implementation for eigenvalue problems of real symmetric matrices.

By definition, an n-dimensional vector x is called an eigenvector of a square matrix A if and only if satisfies the linear equation,

Ax = λx

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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