diagonalization (Meaning)
Wordnet
diagonalization (n)
changing a square matrix to diagonal form (with all non-zero elements on the principal diagonal)
Synonyms & Antonyms of diagonalization
No Synonyms and anytonyms found
diagonalization Sentence Examples
- Diagonalization is a fundamental process in linear algebra used to transform a matrix into a diagonal form.
- The diagonalization of a matrix involves finding a set of eigenvectors that form a basis for the vector space.
- The eigenvalues and eigenvectors play a crucial role in the diagonalization process.
- Through diagonalization, one can simplify matrix operations and computations.
- The theorem on diagonalization states that a square matrix is diagonalizable if and only if it has a full set of linearly independent eigenvectors.
- In practical applications, diagonalization aids in solving systems of linear equations and analyzing dynamic systems.
- Understanding the diagonalization of matrices is essential for solving problems in quantum mechanics and signal processing.
- The process of diagonalization allows us to reveal hidden structures within matrices.
- Diagonalization provides a powerful tool for simplifying complex matrix expressions and calculations.
- Mastery of diagonalization techniques is vital for advanced studies in mathematics, engineering, and physics.
FAQs About the word diagonalization
changing a square matrix to diagonal form (with all non-zero elements on the principal diagonal)
No synonyms found.
No antonyms found.
Diagonalization is a fundamental process in linear algebra used to transform a matrix into a diagonal form.
The diagonalization of a matrix involves finding a set of eigenvectors that form a basis for the vector space.
The eigenvalues and eigenvectors play a crucial role in the diagonalization process.
Through diagonalization, one can simplify matrix operations and computations.
