eigenértékeit

Eigenwert is a German term that translates to "eigenvalue" in English. In mathematics and physics, eigenvalues are a fundamental concept associated with linear transformations or operators. Specifically, for a given square matrix or a linear operator, an eigenvalue is a scalar that, when multiplied by a non-zero vector, results in the same vector scaled by that scalar. This special vector is called an eigenvector.

The relationship can be expressed by the equation Ax = λx, where A is the matrix or operator, x is the eigenvector, and λ (lambda) is the eigenvalue. This equation signifies that applying the transformation A to the vector x only stretches or shrinks x by a factor of λ, without changing its direction. Eigenvalues and eigenvectors are crucial for understanding the behavior of linear systems, diagonalizing matrices, and solving differential equations. They find applications in numerous fields, including quantum mechanics, structural engineering, signal processing, and data analysis (e.g., in principal component analysis). The set of all eigenvalues for a given matrix is called its spectrum.