qr eigen values Algorithm

In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is apply to it. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. Charles-François Sturm developed Fourier's ideas further and bring them to the attention of Cauchy, who combined them with his own ideas and arrived at the fact that real symmetric matrix have real eigenvalues. eigenvalue are often introduced in the context of linear algebra or matrix theory. Around the same time, Francesco Brioschi proved that the eigenvalues of orthogonal matrix lie on the unit circle, and Alfred Clebsch found the corresponding consequence for skew-symmetric matrix.

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