DIAGONAL MATRIX Meaning and
Definition
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A diagonal matrix is a type of square matrix in linear algebra where all the elements that are not on the main diagonal are zero. The main diagonal is a series of elements that starts from the top-left corner of the matrix and extends to the bottom-right corner.
In other words, a diagonal matrix has zeros as its off-diagonal entries. The off-diagonal entries are the elements that are not on the main diagonal. These zeros indicate that there are no interactions or connections between the rows and columns of the matrix, except for those that share the same index.
A diagonal matrix is often represented as a square matrix with n rows and n columns, where n is the number of elements on the main diagonal. It is written in the form of "diag(d₁, d₂, ..., dₙ)", where d₁, d₂, ..., dₙ are the values on the main diagonal.
Diagonal matrices have unique algebraic properties and are frequently used in various mathematical and scientific applications, such as matrix manipulation, solving systems of linear equations, and eigenvalue calculations. Due to their simple structure, diagonal matrices are computationally efficient to work with, as many operations can be simplified or avoided when dealing with these matrices.
Common Misspellings for DIAGONAL MATRIX
- siagonal matrix
- xiagonal matrix
- ciagonal matrix
- fiagonal matrix
- riagonal matrix
- eiagonal matrix
- duagonal matrix
- djagonal matrix
- dkagonal matrix
- doagonal matrix
- d9agonal matrix
- d8agonal matrix
- dizgonal matrix
- disgonal matrix
- diwgonal matrix
- diqgonal matrix
- diafonal matrix
- diavonal matrix
- diabonal matrix
Etymology of DIAGONAL MATRIX
The word "diagonal" comes from the Greek word "diágonios", which means "from corner to corner" or "slanting". The term "matrix" originates from the Latin word "matrix", meaning "mother" or "womb". In mathematics, "matrix" refers to a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Thus, the term "diagonal matrix" describes a matrix where all the elements outside the main diagonal (from the top left to the bottom right) are zero.
Similar spelling words for DIAGONAL MATRIX
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