UNIT MATRIX Meaning and
Definition
-
A unit matrix, also known as an identity matrix, is a square matrix in which all elements on the main diagonal are 1, and all other elements are 0. It is denoted by the symbol "I" or "I_n", where "n" represents the dimension of the matrix. In other words, it is a matrix that has ones along the diagonal and zeros elsewhere, resembling an identity operation.
For example, a 2x2 unit matrix is represented as:
|1 0|
|0 1|
Similarly, a 3x3 unit matrix is represented as:
|1 0 0|
|0 1 0|
|0 0 1|
The unit matrix is significant in linear algebra and plays a crucial role in matrix operations. When a unit matrix is multiplied by any other matrix, the result is the same matrix. It acts as an identity element in matrix multiplication, just like the number 1 is the identity element in multiplicative operations within arithmetic.
Unit matrices have various properties. They are always non-singular, meaning that they have an inverse matrix. The inverse of a unit matrix is itself. Unit matrices are also commutative with respect to addition and multiplication, that is, their order can be interchanged without affecting the result.
The concept of unit matrices finds application and relevance in numerous mathematical and scientific fields, such as linear transformations, determinants, and solving systems of linear equations.
Common Misspellings for UNIT MATRIX
- ynit matrix
- hnit matrix
- jnit matrix
- init matrix
- 8nit matrix
- 7nit matrix
- ubit matrix
- umit matrix
- ujit matrix
- uhit matrix
- unut matrix
- unjt matrix
- unkt matrix
- unot matrix
- un9t matrix
- un8t matrix
- unir matrix
- unif matrix
- unig matrix
Etymology of UNIT MATRIX
The word "unit" in "unit matrix" refers to its property of having ones (or units) along the main diagonal and zeros elsewhere.
The term "unit matrix" itself is derived from the concept of a "unit element" or "identity element" in mathematics. In linear algebra, the unit matrix is also known as the identity matrix, denoted by the symbol "I".
The word "matrix" originated from the Latin word "mātrix", meaning "uterus" or "womb". However, its mathematical usage emerged much later. The modern mathematical definition of a matrix was developed in the mid-19th century. The term "matrix" is used to represent a rectangular arrangement of numbers, symbols, or expressions in rows and columns.
Similar spelling word for UNIT MATRIX
Infographic
Add the infographic to your website:
