In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. The term usually refers to square matrices.An example of a 2-by-2 diagonal matrix is ; the following matrix is a 3-by-3 diagonal matrix: .An identity matrix of any size, or any multiple of it, will be a diagonal matrix.
A diagonal matrix is also a symmetrical matrix. A diagonal matrix in which all the diagonal elements are equal is called a scalar matrix. This kind of matrix is equal to the identity matrix multiplied by a scalar. Diagonal matrices have much simpler rules of addition and multiplication than general square matrices.
Diagonal matrix is a matrix in which non principle diagonal elements are zero. It is not necessary that in diagonal matrix principle diagonal elements must be non zero. Hence square null matrix is also considered as a diagonal matrix. Scalar and unit matrix are special types of diagonal matrices. For more details refer to the video:
In matrix algebra, a diagonal of a square matrix is a set of entries extending from one corner to the farthest corner. There are also other, non-mathematical uses. Non-mathematical uses. A stand of basic scaffolding on a house construction site, with diagonal braces to maintain its structure. In engineering, a ...
Since in general, for , this can be true only if off-diagonal components vanish.Therefore, must be diagonal. Given a diagonal matrix , the matrix power can be computed simply by taking each element to the power in question,
Define diagonal matrix. diagonal matrix synonyms, diagonal matrix pronunciation, diagonal matrix translation, English dictionary definition of diagonal matrix. Noun 1. diagonal matrix - a square matrix with all elements not on the main diagonal equal to zero square matrix - a matrix with the same number of rows and...
Diagonal Matrix. A diagonal matrix matrix is a special kind of symmetric matrix.It is a symmetric matrix with zeros in the off-diagonal elements. Two diagonal matrices are shown below.
Definition of diagonal matrix in the AudioEnglish.org Dictionary. Meaning of diagonal matrix. What does diagonal matrix mean? Proper usage and pronunciation (in phonetic transcription) of the word diagonal matrix. Information about diagonal matrix in the AudioEnglish.org dictionary, synonyms and antonyms.
The diagonal from the top left corner to the bottom right corner of a square matrix is called the main diagonal or leading diagonal. The other diagonal from the top right to the bottom left corner is called antidiagonal or counterdiagonal. You can also define the main diagonal and antidiagonal of a rectangular matrix. See here for more.