Eigenvalue Of A Square 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 eigenvalue of a square matrix represents a scalar value by which the eigenvector is scaled when the matrix is multiplied by it.
- Linear transformations may be represented by matrices, and the eigenvalue of a square matrix is one of the critical parameters involved in such transformations.
- One of the key steps to analyzing a square matrix is computing its eigenvalue, which requires finding roots of a characteristic polynomial.
- Finding the eigenvalue of a square matrix is essential in understanding how the matrix transforms input data and which directions in the input space are stretched the most.
- Mathematical methods including numerical algorithms are used to find the eigenvalue of a square matrix and understanding the characteristics of different types of matrices.