Block Diagonal Matrix
The term “block matrix” refers to a matrix that is divided into blocks. In such matrices, the non-diagonal blocks are zero matrices, whereas the main diagonal blocks are square matrices. A matrix “A = [aij]” is called a block diagonal matrix when aij = 0, for i ≠ j, i.e., when the non-diagonal blocks are zero.
[Tex]A = \left[\begin{array}{cccccc} a_{11} & 0 & 0 & . & . & 0\\ 0 & a_{22} & 0 & . & . & 0\\ 0 & 0 & a_{33} & . & . & 0\\ . & . & . & . & . & .\\ . & . & . & . & . & .\\ 0 & 0 & 0 & . & . & a_{nn} \end{array}\right]_{n\times n} [/Tex]
Diagonal Matrix
Diagonal Matrix is a matrix in which all the non-diagonal elements are zero. A matrix is defined as a rectangular array of numbers that are arranged in rows and columns. The size of a matrix can be determined by the number of rows and columns in it. A matrix is said to be an “m by n” matrix when it has “m” rows and “n” columns and is written as an “m × n” matrix.
For example, the order of the matrix that has five rows and four columns is “5 × 4.” We have different types of matrices, such as rectangular, square, triangular, symmetric, singular, etc. The image given below is an “m × n” matrix that has “m” rows and “n” columns.
Table of Content
- What is a Diagonal Matrix?
- Examples of a Diagonal Matrix
- Properties of a Diagonal Matrix
- Block Diagonal Matrix
- Determinant of a Diagonal Matrix
- Inverse of a Diagonal Matrix
- Anti-Diagonal Matrix