In linear algebra, the Eigenvectors of a lineal operator are the non-zero vectors that, when transformed by the operator, they give an escalar multiple of themselves, meeaning their direction is not changed. This scalar is called EigenValue. Normally, the transformation is completely determined by its EigenVectors and EigenValues. The joining of the EigenVectors with a common EigenValue is called and EigenSpace.
In the example of the famous drawring Mona Lisa by da Vinci, the image has been transformed and has been deformed in such a way that it's vertical axis has not changed.The blue vector which goes from the chest to the shoulder has changed direction, while the red vector hasn´t. This means that the red vector is, therefore, an EigenVector of the transformation, while the blue vector isn´t. Because the red vector hasn´t changed in lenght, its EigenValue is 1. Every single vector in this direction are EigenVectors, with the same EigenValue. This makes the EigenSpace for this EigenValue.
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