Eigenvalue (Noun)
Meaning
(mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant.
Classification
Nouns denoting cognitive processes and contents.
Examples
- The eigenvalue of a matrix is a scalar that represents how much change occurs in a linear transformation.
- To find the eigenvalues of a matrix, we set the characteristic equation equal to zero and solve for the variable.
- In linear algebra, eigenvalues are used to describe the amount of change in a linear transformation, with higher eigenvalues indicating more change.
- The eigenvalue decomposition of a matrix is a factorization of the matrix into a product of three matrices, including a diagonal matrix of eigenvalues.
- If a matrix has a zero eigenvalue, it is singular and does not have an inverse.