diagonalisation (Meaning)
Wordnet
diagonalisation (n)
changing a square matrix to diagonal form (with all non-zero elements on the principal diagonal)
Synonyms & Antonyms of diagonalisation
No Synonyms and anytonyms found
diagonalisation Sentence Examples
- Diagonalisation is a process in linear algebra used to transform a matrix into a diagonal form.
- The process of diagonalisation involves finding a set of eigenvectors that form a basis for the vector space.
- Once diagonalised, the matrix will have non-zero elements only along its diagonal.
- Diagonalisation simplifies various computations such as matrix exponentiation and finding powers of the matrix.
- Eigenvalues play a crucial role in the diagonalisation process.
- In quantum mechanics, diagonalisation is essential for finding the energy levels of a system described by a Hamiltonian matrix.
- The diagonalisation of a symmetric matrix results in a set of orthogonal eigenvectors.
- Researchers often use diagonalisation techniques to solve differential equations with constant coefficients.
- Diagonalisation is a fundamental concept in many areas of mathematics and physics.
- Computer algorithms for diagonalisation are implemented in software packages like MATLAB and Python to facilitate numerical computations.
FAQs About the word diagonalisation
changing a square matrix to diagonal form (with all non-zero elements on the principal diagonal)
No synonyms found.
No antonyms found.
Diagonalisation is a process in linear algebra used to transform a matrix into a diagonal form.
The process of diagonalisation involves finding a set of eigenvectors that form a basis for the vector space.
Once diagonalised, the matrix will have non-zero elements only along its diagonal.
Diagonalisation simplifies various computations such as matrix exponentiation and finding powers of the matrix.
