diagonal matrix (Meaning)
Wordnet
diagonal matrix (n)
a square matrix with all elements not on the main diagonal equal to zero
Synonyms & Antonyms of diagonal matrix
No Synonyms and anytonyms found
diagonal matrix Sentence Examples
- In linear algebra, a diagonal matrix is a square matrix where all elements off the main diagonal are zero.
- A diagonal matrix can be represented as a matrix with non-zero elements only along the diagonal.
- The identity matrix is a special case of a diagonal matrix where all diagonal elements are equal to 1.
- Multiplying a diagonal matrix by a scalar results in scaling the diagonal elements by that scalar.
- Diagonal matrices are useful in various mathematical operations, such as matrix multiplication and determinant calculation.
- When performing operations like addition or multiplication, diagonal matrices exhibit unique properties that simplify computations.
- Eigenvalues of a diagonal matrix are simply its diagonal elements.
- Diagonal matrices are often employed in computer graphics and numerical simulations due to their efficiency in computations.
- A diagonal matrix can represent a system of linear equations with independent variables.
- Spectral decomposition involves expressing a matrix as a product of diagonal and orthogonal matrices.
FAQs About the word diagonal matrix
a square matrix with all elements not on the main diagonal equal to zero
No synonyms found.
No antonyms found.
In linear algebra, a diagonal matrix is a square matrix where all elements off the main diagonal are zero.
A diagonal matrix can be represented as a matrix with non-zero elements only along the diagonal.
The identity matrix is a special case of a diagonal matrix where all diagonal elements are equal to 1.
Multiplying a diagonal matrix by a scalar results in scaling the diagonal elements by that scalar.
