EIGENVALUES Meaning and
Definition
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Eigenvalues are a fundamental concept in linear algebra, used to describe certain properties of matrices. More specifically, they are the values that satisfy a particular mathematical equation related to a given matrix.
In simpler terms, eigenvalues are the unique scalars that, when multiplied by a given matrix, result in a nonzero vector that is parallel to the original vector. In other words, they represent the scaling factor by which a vector is stretched or compressed when acted upon by the matrix.
Mathematically, the eigenvalues of a square matrix are found by solving the characteristic equation, which is obtained by subtracting an identity matrix from the matrix being considered, and then computing its determinant. The roots of this equation correspond to the eigenvalues of the matrix.
Eigenvalues have significant applications in a variety of fields, such as physics, engineering, and computer science. They provide valuable insights into the behavior of linear transformations and systems, including stability, oscillations, convergence, and the motion of dynamic systems. Additionally, eigenvalues are closely linked with eigenvectors, which are the corresponding independent vectors associated with each eigenvalue. Eigenvectors and eigenvalues provide a powerful basis for analyzing and solving complex systems, making the study of eigenvalues essential in many mathematical and scientific disciplines.
Common Misspellings for EIGENVALUES
- wigenvalues
- sigenvalues
- digenvalues
- rigenvalues
- 4igenvalues
- 3igenvalues
- eugenvalues
- ejgenvalues
- ekgenvalues
- eogenvalues
- e9genvalues
- e8genvalues
- eifenvalues
- eivenvalues
- eibenvalues
- eihenvalues
- eiyenvalues
- eitenvalues
- eigwnvalues
- eigsnvalues
Etymology of EIGENVALUES
The word "eigenvalues" originates from the German term "eigenwerte". It was coined by the German mathematician David Hilbert in 1904. The prefix "eigen" in German means "own" or "intrinsic", while "wert" means "value". Therefore, "eigenwerte" can be translated as "intrinsic values" or "own values". The term was later adopted in the English language, becoming "eigenvalues", to refer to the specific values associated with linear transformations or matrices.
