unit matrix (Meaning)
Wordnet
unit matrix (n)
a scalar matrix in which all of the diagonal elements are unity
Synonyms & Antonyms of unit matrix
No Synonyms and anytonyms found
unit matrix Sentence Examples
- The unit matrix, an identity matrix with all diagonal elements equal to one, represents the neutral element under matrix multiplication.
- A unit matrix of order n has all its off-diagonal elements set to zero and diagonal elements to one.
- The multiplicative inverse of a unit matrix is itself, resulting in a simplified calculation.
- When a matrix is multiplied by a unit matrix, the original matrix remains unchanged.
- The determinant of a unit matrix is always one, making it a useful tool for solving certain types of equations.
- In linear algebra, the unit matrix serves as the identity element for matrix operations.
- Eigenvalues of a unit matrix are all equal to one, providing a unique property for solving specific problems.
- The unit matrix often serves as a placeholder or default value in matrix manipulations and algorithms.
- In computer graphics, a unit matrix can represent a transformation where no translation, rotation, or scaling occurs.
- The concept of a unit matrix extends to other mathematical structures, such as group theory and ring theory, where it plays a fundamental role.
FAQs About the word unit matrix
a scalar matrix in which all of the diagonal elements are unity
No synonyms found.
No antonyms found.
The unit matrix, an identity matrix with all diagonal elements equal to one, represents the neutral element under matrix multiplication.
A unit matrix of order n has all its off-diagonal elements set to zero and diagonal elements to one.
The multiplicative inverse of a unit matrix is itself, resulting in a simplified calculation.
When a matrix is multiplied by a unit matrix, the original matrix remains unchanged.
