Diagonalize (Verb)
Meaning
Transform a matrix to a diagonal matrix.
Classification
Verbs of size, temperature change, intensifying, etc..
Examples
- To diagonalize the matrix, the eigenvalues and corresponding eigenvectors are first calculated using a suitable algorithm from linear algebra.
- Diagonalizing a matrix is essential for solving homogeneous systems of linear differential equations with constant coefficients.
- In many applications, a matrix can be diagonalized using an orthogonal similarity transformation.
- However, for singular matrices, it may not be possible to diagonalize them in the conventional sense due to the existence of zero eigenvalues.
- Modern methods can effectively diagonalize large matrices efficiently using iterative techniques.