In a particular linear transformation, the directions that are flipped, compressed, or stretched are called eigenvectors.
The vast majority of libraries, including Numpy, return eigenvectors that have been scaled to have a length of 1. (called unit vectors). When x is multiplied by A, eigenvalue indicates how much x is scaled, stretched, contracted, reversible, or unaffected. At most, there are n dimensions and n eigenvalues.
An eigenvector in mathematics is equivalent to real non-zero eigenvalues that point in the direction extended by the transformation, whereas an eigenvalue is thought of as a factor by which it is stretched. The transformation's direction is reversed if the eigenvalue is negative.
Eigenvectors are the directions that a specific linear transformation flips, compresses, or stretches. The strength of the transformation in the direction of the eigenvector or the compression factor is referred to as the eigenvalue.
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