Diagonalisation (Noun)
Meaning
Changing a square matrix to diagonal form (with all non-zero elements on the principal diagonal); "the diagonalization of a normal matrix by a unitary transformation".
Classification
Nouns denoting cognitive processes and contents.
Examples
- Diagonalisation is the process used in linear algebra to simplify square matrices, where non-zero entries occur only on the main diagonal.
- Through a change of basis using the eigenvectors of a square matrix, it becomes possible to express a linear transformation by the method of diagonalisation.
- Hermitian and real symmetric matrices always can undergo complete diagonalisation and even specialise a new theory when specifically classified together into standard formats to construct possible outputs which conform specific axioms needed later by theorists also creating classifications needing comparisons known such axiomatic math data forms.
- Ultimately when trying to completely diagonalise and perform linear transformation methods on either square matrices Hermitian cases like or other symmetric form units may lose their original form, change or be distorted for convenience.
- When mathematicians refer to the diagonalisation of a matrix, all the properties and characteristics found on the resulting diagonalised form are found by keeping transformations equivalent and for symmetry preservation.