SCALAR MATRIX Meaning and
Definition
-
A scalar matrix is a square matrix in which all the elements on the main diagonal are equal to a certain scalar, and all the other elements are zero. In other words, a scalar matrix is a diagonal matrix with equal scalar elements along the diagonal.
Formally, let A be an n x n matrix. If A is a scalar matrix, then A can be represented as:
A = λI
where λ is a scalar, I is the identity matrix of size n x n, and A and I have the same dimensions. The scalar λ is the value that every element on the main diagonal of A takes.
The main diagonal of a matrix refers to the elements that run from the top left corner to the bottom right corner of the matrix. Therefore, in a scalar matrix, all elements on the main diagonal are equal to λ, while all other elements outside the diagonal are zero.
Scalar matrices are particularly notable for their simplicity and certain mathematical properties. For example, scalar matrices have the same eigenvalues as the scalar value λ, and the determinant of a scalar matrix is equal to λ raised to the power of n, where n is the dimension of the matrix. Scalar matrices also commute with other matrices, meaning it doesn't matter in which order they are multiplied.
Common Misspellings for SCALAR MATRIX
- acalar matrix
- zcalar matrix
- xcalar matrix
- dcalar matrix
- ecalar matrix
- wcalar matrix
- sxalar matrix
- svalar matrix
- sfalar matrix
- sdalar matrix
- sczlar matrix
- scslar matrix
- scwlar matrix
- scqlar matrix
- scakar matrix
- scapar matrix
- scaoar matrix
- scalzr matrix
- scalsr matrix
Etymology of SCALAR MATRIX
The word "scalar" comes from the Latin word "scalaris", which means "pertaining to a ladder". It is derived from the Latin word "scala", meaning "a ladder or stairway". The term "matrix" has its roots in the Latin word "mater" or "matris", meaning "mother". In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
Therefore, the term "scalar matrix" combines the usage of "scalar" to denote a mathematical quantity (a single number) and "matrix" to refer to the rectangular arrangement of numbers. A scalar matrix is a specific type of matrix where the diagonal elements (the elements from the top left to bottom right) are all equal, and the rest of the matrix contains zeros.
Similar spelling words for SCALAR MATRIX
Infographic
Add the infographic to your website:
