diagonalisation Synonyms

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diagonalisation Meaning

Wordnet

diagonalisation (n)

changing a square matrix to diagonal form (with all non-zero elements on the principal diagonal)

diagonalisation Sentence Examples

  1. Diagonalisation is a process in linear algebra used to transform a matrix into a diagonal form.
  2. The process of diagonalisation involves finding a set of eigenvectors that form a basis for the vector space.
  3. Once diagonalised, the matrix will have non-zero elements only along its diagonal.
  4. Diagonalisation simplifies various computations such as matrix exponentiation and finding powers of the matrix.
  5. Eigenvalues play a crucial role in the diagonalisation process.
  6. In quantum mechanics, diagonalisation is essential for finding the energy levels of a system described by a Hamiltonian matrix.
  7. The diagonalisation of a symmetric matrix results in a set of orthogonal eigenvectors.
  8. Researchers often use diagonalisation techniques to solve differential equations with constant coefficients.
  9. Diagonalisation is a fundamental concept in many areas of mathematics and physics.
  10. 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.