diagonal matrix Sentence Examples

  1. In linear algebra, a diagonal matrix is a square matrix where all elements off the main diagonal are zero.
  2. A diagonal matrix can be represented as a matrix with non-zero elements only along the diagonal.
  3. The identity matrix is a special case of a diagonal matrix where all diagonal elements are equal to 1.
  4. Multiplying a diagonal matrix by a scalar results in scaling the diagonal elements by that scalar.
  5. Diagonal matrices are useful in various mathematical operations, such as matrix multiplication and determinant calculation.
  6. When performing operations like addition or multiplication, diagonal matrices exhibit unique properties that simplify computations.
  7. Eigenvalues of a diagonal matrix are simply its diagonal elements.
  8. Diagonal matrices are often employed in computer graphics and numerical simulations due to their efficiency in computations.
  9. A diagonal matrix can represent a system of linear equations with independent variables.
  10. Spectral decomposition involves expressing a matrix as a product of diagonal and orthogonal matrices.

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

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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.