Definition of Diagonalizable. Meaning of Diagonalizable. Synonyms of Diagonalizable

- In linear algebra, a square matrix A {\displaystyle A}  is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there...
- algebraic group is said to be diagonalizable if it is isomorphic to a subgroup of Dn, the group of diagonal matrices. A diagonalizable group defined over a field...
- matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized...
- matrix A satisfying the equation A*A = AA* is diagonalizable. (The converse does not hold because diagonalizable matrices may have non-orthogonal eigenspaces...
- converse is also true; that is, if two diagonalizable matrices commute, they are simultaneously diagonalizable. But if you take any two matrices that...
- does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n {\displaystyle n\times n} matrix is defective...
- linearly independent eigenvectors. Not all matrices are diagonalizable; matrices that are not diagonalizable are called defective matrices. Consider the following...
- are said to be diagonalizable. More generally, an endomorphism and a matrix are also said diagonalizable, if they become diagonalizable after extending...
- endomorphism φ of a finite-dimensional vector space over a field F is diagonalizable if and only if its minimal polynomial factors completely over F into...
- eigendecomposition (or spectral decomposition) of a diagonalizable matrix is a decomposition of a diagonalizable matrix into a specific canonical form whereby...