Eigenvalue Of A Matrix (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 characteristic equation used to find the eigenvalues of a matrix is det(A - λI) = 0, where A is the matrix, λ is the eigenvalue, and I is the identity matrix.
- In linear algebra, the set of eigenvalues of a matrix A is often used to describe the properties of linear transformations given by A.
- The eigenvalue of a matrix represents how much change occurs in a linear transformation - a larger eigenvalue indicates more change and a smaller eigenvalue indicates less change.
- Determining the eigenvalues of a matrix is one approach to solving systems of linear differential equations.
- The eigenvalue decomposition of a matrix A allows us to express A as the product of three matrices: one whose columns are the eigenvectors of A, a diagonal matrix containing the eigenvalues of A, and the inverse of the first matrix.